Pub Date : 2026-07-01Epub Date: 2026-02-06DOI: 10.1016/j.na.2026.114072
Márcio Batista, Allan Kenedy
In this paper, we introduce an energy functional that characterizes, from a variational perspective, compact capillary linear Weingarten hypersurfaces in the half-space. We then derive the second variation of this functional and naturally define a notion of stability in this context. Finally, we demonstrate that, under suitable conditions, spherical caps in the half-space are the only stable compact capillary linear Weingarten hypersurfaces.
{"title":"Stable Capillary linear Weingarten hypersurfaces in the half-space","authors":"Márcio Batista, Allan Kenedy","doi":"10.1016/j.na.2026.114072","DOIUrl":"10.1016/j.na.2026.114072","url":null,"abstract":"<div><div>In this paper, we introduce an energy functional that characterizes, from a variational perspective, compact capillary linear Weingarten hypersurfaces in the half-space. We then derive the second variation of this functional and naturally define a notion of stability in this context. Finally, we demonstrate that, under suitable conditions, spherical caps in the half-space are the only stable compact capillary linear Weingarten hypersurfaces.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"268 ","pages":"Article 114072"},"PeriodicalIF":1.3,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-01Epub Date: 2026-02-11DOI: 10.1016/j.na.2026.114076
Mirela Kohr , Radu Precup
We analyze a control problem for a general class of coupled systems of stationary Navier-Stokes type equations in the incompressible case, with homogeneous Dirichlet condition on the boundary of a bounded domain in , N ≤ 3, and non-homogeneous terms of reaction type. Such a control problem may describe the flow of a viscous incompressible fluid in multidisperse porous media with a controllability condition imposed on the coefficients of the coupled systems and expressed by means of a continuous functional depending on the velocities and pressures. The controllability conditions are not necessarily given by equalities, but more generally are formulated by inclusions. A lower and upper solution technique is used for the exact and approximate solvability of the control problem, which requires the existence, uniqueness and continuous dependence of the solution on the coefficients.
{"title":"Navier-Stokes type models with control conditions given by inclusions","authors":"Mirela Kohr , Radu Precup","doi":"10.1016/j.na.2026.114076","DOIUrl":"10.1016/j.na.2026.114076","url":null,"abstract":"<div><div>We analyze a control problem for a general class of coupled systems of stationary Navier-Stokes type equations in the incompressible case, with homogeneous Dirichlet condition on the boundary of a bounded domain in <span><math><msup><mi>R</mi><mi>N</mi></msup></math></span>, <em>N</em> ≤ 3, and non-homogeneous terms of reaction type. Such a control problem may describe the flow of a viscous incompressible fluid in multidisperse porous media with a controllability condition imposed on the coefficients of the coupled systems and expressed by means of a continuous functional depending on the velocities and pressures. The controllability conditions are not necessarily given by equalities, but more generally are formulated by inclusions. A lower and upper solution technique is used for the exact and approximate solvability of the control problem, which requires the existence, uniqueness and continuous dependence of the solution on the coefficients.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"268 ","pages":"Article 114076"},"PeriodicalIF":1.3,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-01Epub Date: 2026-02-06DOI: 10.1016/j.na.2026.114074
Yingfang Zhang, Wenming Zou
We study the stability of a class of Caffarelli-Kohn-Nirenberg (CKN) interpolation inequality and establish a strong-form stability as following:where for and for p > 2, and δp,a,b(u) is deficit of the CKN. We also note that it is impossible to establish stability results for or individually. Moreover, we consider the second-order CKN inequalities and establish similar results for radial functions.
{"title":"A strong-form stability for a class of Lp Caffarelli-Kohn-Nirenberg interpolation inequality","authors":"Yingfang Zhang, Wenming Zou","doi":"10.1016/j.na.2026.114074","DOIUrl":"10.1016/j.na.2026.114074","url":null,"abstract":"<div><div>We study the stability of a class of Caffarelli-Kohn-Nirenberg (CKN) interpolation inequality and establish a strong-form stability as following:<span><span><span><math><mrow><munder><mi>inf</mi><mrow><mi>v</mi><mo>∈</mo><msub><mi>M</mi><mrow><mi>p</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>b</mi></mrow></msub></mrow></munder><mfrac><mrow><msub><mrow><mo>∥</mo><mi>u</mi><mo>−</mo><mi>v</mi><mo>∥</mo></mrow><msubsup><mi>H</mi><mi>b</mi><mi>p</mi></msubsup></msub><msubsup><mrow><mo>∥</mo><mi>u</mi><mo>−</mo><mi>v</mi><mo>∥</mo></mrow><mrow><msubsup><mi>L</mi><mi>a</mi><mi>p</mi></msubsup></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msubsup></mrow><mrow><msub><mrow><mo>∥</mo><mi>u</mi><mo>∥</mo></mrow><msubsup><mi>H</mi><mi>b</mi><mi>p</mi></msubsup></msub><msubsup><mrow><mo>∥</mo><mi>u</mi><mo>∥</mo></mrow><mrow><msubsup><mi>L</mi><mi>a</mi><mi>p</mi></msubsup></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msubsup></mrow></mfrac><mo>≤</mo><mi>C</mi><msub><mi>δ</mi><mrow><mi>p</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>b</mi></mrow></msub><msup><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mi>t</mi></msup><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mi>t</mi><mo>=</mo><mn>1</mn></mrow></math></span> for <span><math><mrow><mi>p</mi><mo>=</mo><mn>2</mn></mrow></math></span> and <span><math><mrow><mi>t</mi><mo>=</mo><mfrac><mn>1</mn><mi>p</mi></mfrac></mrow></math></span> for <em>p</em> > 2, and <em>δ</em><sub><em>p,a,b</em></sub>(<em>u</em>) is deficit of the CKN. We also note that it is impossible to establish stability results for <span><math><msub><mrow><mo>∥</mo><mo>·</mo><mo>∥</mo></mrow><msubsup><mi>H</mi><mi>b</mi><mi>p</mi></msubsup></msub></math></span> or <span><math><msub><mrow><mo>∥</mo><mo>·</mo><mo>∥</mo></mrow><msubsup><mi>L</mi><mi>a</mi><mi>p</mi></msubsup></msub></math></span> individually. Moreover, we consider the second-order CKN inequalities and establish similar results for radial functions.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"268 ","pages":"Article 114074"},"PeriodicalIF":1.3,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-01Epub Date: 2026-02-12DOI: 10.1016/j.na.2026.114078
Hyungsung Yun
We establish the optimal regularity of viscosity solutions towhich arises in the regularity theory of the porous medium equation. Specifically, we prove that under the zero Dirichlet boundary condition on , the optimal regularity of u up to the flat boundary is . Moreover, for the homogeneous equations, we establish that the optimal regularity of u is in the spatial variables, and that is smooth in the variables x′ and t.
{"title":"Optimal regularity for degenerate parabolic equations on a flat boundary","authors":"Hyungsung Yun","doi":"10.1016/j.na.2026.114078","DOIUrl":"10.1016/j.na.2026.114078","url":null,"abstract":"<div><div>We establish the optimal regularity of viscosity solutions to<span><span><span><math><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>−</mo><msubsup><mi>x</mi><mi>n</mi><mi>γ</mi></msubsup><mstyle><mi>Δ</mi></mstyle><mi>u</mi><mo>=</mo><mi>f</mi><mo>,</mo></mrow></math></span></span></span>which arises in the regularity theory of the porous medium equation. Specifically, we prove that under the zero Dirichlet boundary condition on <span><math><mrow><mo>{</mo><msub><mi>x</mi><mi>n</mi></msub><mo>=</mo><mn>0</mn><mo>}</mo></mrow></math></span>, the optimal regularity of <em>u</em> up to the flat boundary <span><math><mrow><mo>{</mo><msub><mi>x</mi><mi>n</mi></msub><mo>=</mo><mn>0</mn><mo>}</mo></mrow></math></span> is <span><math><msup><mi>C</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>−</mo><mi>γ</mi></mrow></msup></math></span>. Moreover, for the homogeneous equations, we establish that the optimal regularity of <em>u</em> is <span><math><msup><mi>C</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>−</mo><mi>γ</mi></mrow></msup></math></span> in the spatial variables, and that <span><math><mrow><msubsup><mi>x</mi><mi>n</mi><mrow><mo>−</mo><mi>γ</mi></mrow></msubsup><mi>u</mi></mrow></math></span> is smooth in the variables <em>x</em>′ and <em>t</em>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"268 ","pages":"Article 114078"},"PeriodicalIF":1.3,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-01Epub Date: 2026-01-29DOI: 10.1016/j.na.2026.114062
Jing Li
The purpose of this paper is to investigate the vanishing theorems problem of a generalized harmonic map in a class of sub-Riemannian manifolds. More specifically, we consider a horizontal functional related to the pullback metrics and introduce the concept of (weakly) stationary maps with potential H into Heisenberg groups. By using the stress-energy tensor method, we achieve some vanishing theorems for these maps under diverse proper conditions respectively.
{"title":"Vanishing theorems for F−CC stationary maps with potential into Heisenberg groups","authors":"Jing Li","doi":"10.1016/j.na.2026.114062","DOIUrl":"10.1016/j.na.2026.114062","url":null,"abstract":"<div><div>The purpose of this paper is to investigate the vanishing theorems problem of a generalized harmonic map in a class of sub-Riemannian manifolds. More specifically, we consider a horizontal functional <span><math><msubsup><mstyle><mi>Φ</mi></mstyle><mrow><mi>H</mi><mo>,</mo><mi>H</mi><mo>,</mo><mi>D</mi></mrow><mi>F</mi></msubsup></math></span> related to the pullback metrics and introduce the concept of (weakly) <span><math><mrow><mi>F</mi><mspace></mspace><mo>−</mo><mspace></mspace><mi>C</mi><mi>C</mi></mrow></math></span> stationary maps with potential <em>H</em> into Heisenberg groups. By using the stress-energy tensor method, we achieve some vanishing theorems for these maps under diverse proper conditions respectively.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"268 ","pages":"Article 114062"},"PeriodicalIF":1.3,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146070768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-01Epub Date: 2026-02-07DOI: 10.1016/j.na.2026.114075
Zhenghuan Gao
In this paper, we study an overdetermined problem for the so-called -Hessian equations, which include the classical k-Hessian equations and p-Laplace equations as special cases. We prove the symmetry of the solutions by establishing a Rellich-Pohozaev type identity.
{"title":"A serrin-type overdetermined problem for a class of fully nonlinear elliptic equations","authors":"Zhenghuan Gao","doi":"10.1016/j.na.2026.114075","DOIUrl":"10.1016/j.na.2026.114075","url":null,"abstract":"<div><div>In this paper, we study an overdetermined problem for the so-called <span><math><mrow><mi>p</mi><mspace></mspace><mo>−</mo><mspace></mspace><mi>k</mi></mrow></math></span>-Hessian equations, which include the classical <em>k</em>-Hessian equations and <em>p</em>-Laplace equations as special cases. We prove the symmetry of the solutions by establishing a Rellich-Pohozaev type identity.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"268 ","pages":"Article 114075"},"PeriodicalIF":1.3,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-01Epub Date: 2026-02-13DOI: 10.1016/j.na.2026.114080
Francesca Crispo , Angelica Pia Di Feola , Carlo Romano Grisanti
The paper is concerned with the 3D-initial value problem for power-law fluids with shear dependent viscosity in a spatially periodic domain. The goal is the construction of a weak solution enjoying an energy equality. The results hold assuming an initial data v0 ∈ J2(Ω) and for . It is interesting to observe that the result is in complete agreement with the one known for the Navier-Stokes equations. Further, in both cases, the additional dissipation, which measures the possible gap with the classical energy equality, is only expressed in terms of energy quantities.
{"title":"Estimates of a possible gap related to the energy equality for a class of non-Newtonian fluids","authors":"Francesca Crispo , Angelica Pia Di Feola , Carlo Romano Grisanti","doi":"10.1016/j.na.2026.114080","DOIUrl":"10.1016/j.na.2026.114080","url":null,"abstract":"<div><div>The paper is concerned with the 3D-initial value problem for power-law fluids with shear dependent viscosity in a spatially periodic domain. The goal is the construction of a weak solution enjoying an energy equality. The results hold assuming an initial data <em>v</em><sub>0</sub> ∈ <em>J</em><sup>2</sup>(Ω) and for <span><math><mrow><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mfrac><mn>9</mn><mn>5</mn></mfrac><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>. It is interesting to observe that the result is in complete agreement with the one known for the Navier-Stokes equations. Further, in both cases, the additional dissipation, which measures the possible gap with the classical energy equality, is only expressed in terms of energy quantities.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"268 ","pages":"Article 114080"},"PeriodicalIF":1.3,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-01Epub Date: 2026-02-04DOI: 10.1016/j.na.2026.114073
Giovanni Giliberti
This paper is concerned with the study of delay evolution equations with non-local, multivalued initial conditions. We provide existence results for mild solutions in abstract Banach spaces with uniformly convex dual. Both cases in which the semigroup generated is non-compact and compact are analysed, with the discussion later extended to infinite time intervals. The approach relies on topological methods–such as topological degree and continuation principles–integrated with measures of non-compactness, which allow us to overcome the lack of compactness of the operators. Moreover, explicit examples of non-local multivalued initial conditions are presented, with applications to transport equations and reaction-diffusion systems.
{"title":"Delay evolution equations with non-local multivalued initial conditions","authors":"Giovanni Giliberti","doi":"10.1016/j.na.2026.114073","DOIUrl":"10.1016/j.na.2026.114073","url":null,"abstract":"<div><div>This paper is concerned with the study of delay evolution equations with non-local, multivalued initial conditions. We provide existence results for mild solutions in abstract Banach spaces with uniformly convex dual. Both cases in which the semigroup generated is non-compact and compact are analysed, with the discussion later extended to infinite time intervals. The approach relies on topological methods–such as topological degree and continuation principles–integrated with measures of non-compactness, which allow us to overcome the lack of compactness of the operators. Moreover, explicit examples of non-local multivalued initial conditions are presented, with applications to transport equations and reaction-diffusion systems.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"268 ","pages":"Article 114073"},"PeriodicalIF":1.3,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-01Epub Date: 2026-01-29DOI: 10.1016/j.na.2026.114060
Jonas Stange
We study a bulk-surface Cahn–Hilliard model with non-degenerate mobility and singular potentials in two dimensions. Following the ideas of the recent work by Conti, Galimberti, Gatti, and Giorgini [Calc. Var. Partial Differential Equations, 64(3):Paper No. 87, 32, 2025] for the Cahn–Hilliard equation with homogeneous Neumann boundary conditions, we show the uniqueness of weak solutions together with a continuous dependence estimate for sufficiently regular mobility functions. Next, under weaker assumptions on the mobility functions, we show the existence of a weak solution that exhibits the propagation of uniform-in-time regularity and satisfies the instantaneous separation property. Lastly, we consider the long-time behavior and prove that the unique weak solution converges to a solution of the stationary bulk-surface Cahn–Hilliard equation. Our approach for the uniqueness proof relies on a new well-posedness and regularity theory for a bulk-surface elliptic system with non-constant coefficients, which may be of independent interest.
{"title":"Well-posedness and long-time behavior of a bulk-surface Cahn–Hilliard model with non-degenerate mobility","authors":"Jonas Stange","doi":"10.1016/j.na.2026.114060","DOIUrl":"10.1016/j.na.2026.114060","url":null,"abstract":"<div><div>We study a bulk-surface Cahn–Hilliard model with non-degenerate mobility and singular potentials in two dimensions. Following the ideas of the recent work by Conti, Galimberti, Gatti, and Giorgini [Calc. Var. Partial Differential Equations, 64(3):Paper No. 87, 32, 2025] for the Cahn–Hilliard equation with homogeneous Neumann boundary conditions, we show the uniqueness of weak solutions together with a continuous dependence estimate for sufficiently regular mobility functions. Next, under weaker assumptions on the mobility functions, we show the existence of a weak solution that exhibits the propagation of uniform-in-time regularity and satisfies the instantaneous separation property. Lastly, we consider the long-time behavior and prove that the unique weak solution converges to a solution of the stationary bulk-surface Cahn–Hilliard equation. Our approach for the uniqueness proof relies on a new well-posedness and regularity theory for a bulk-surface elliptic system with non-constant coefficients, which may be of independent interest.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"268 ","pages":"Article 114060"},"PeriodicalIF":1.3,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146070767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-05DOI: 10.1016/j.na.2025.114054
Daniel Goodair
We obtain energy estimates for a transport and stretching noise under Leray Projection on a 2D bounded convex domain, in Sobolev Spaces of arbitrarily high order. The estimates are taken in equivalent inner products, defined through powers of the Stokes Operator with a specific choice of Navier boundary conditions. We exploit fine properties of the noise in relation to the Stokes Operator to achieve cancellation of derivatives in the presence of the Leray Projector. As a result, we achieve an additional degree of regularity in the corresponding Stochastic Navier-Stokes Equation to attain a true strong solution of the original Stratonovich equation. Furthermore for any order of smoothness, we can construct a strong solution of a hyperdissipative version of the Stochastic Navier-Stokes Equation with the given regularity; hyperdissipation is only required to control the nonlinear term in the presence of a boundary. We supplement the result by obtaining smoothness without hyperdissipation on the torus, in 2D and 3D on the lifetime of solutions.
{"title":"High order smoothness for stochastic Navier-Stokes equations with transport and stretching noise on bounded domains","authors":"Daniel Goodair","doi":"10.1016/j.na.2025.114054","DOIUrl":"10.1016/j.na.2025.114054","url":null,"abstract":"<div><div>We obtain energy estimates for a transport and stretching noise under Leray Projection on a 2D bounded convex domain, in Sobolev Spaces of arbitrarily high order. The estimates are taken in equivalent inner products, defined through powers of the Stokes Operator with a specific choice of Navier boundary conditions. We exploit fine properties of the noise in relation to the Stokes Operator to achieve cancellation of derivatives in the presence of the Leray Projector. As a result, we achieve an additional degree of regularity in the corresponding Stochastic Navier-Stokes Equation to attain a true strong solution of the original Stratonovich equation. Furthermore for any order of smoothness, we can construct a strong solution of a hyperdissipative version of the Stochastic Navier-Stokes Equation with the given regularity; hyperdissipation is only required to control the nonlinear term in the presence of a boundary. We supplement the result by obtaining smoothness without hyperdissipation on the torus, in 2D and 3D on the lifetime of solutions.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"267 ","pages":"Article 114054"},"PeriodicalIF":1.3,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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