Abstract We establish fine bounds for best constants of the fractional subcritical Sobolev embeddings W0s,p(Ω)↪Lq(Ω), {W}_{0}^{s,p}(Omega )hspace{0.33em}hookrightarrow hspace{0.33em}{L}^{q}(Omega ), where N≥1 Nge 1 , 0<s<1 0lt slt 1 , p=1,2 p=1,2 , 1≤q<ps∗=NpN−sp 1le qlt {p}_{s}^{ast }=frac{Np}{N-sp} , and Ω⊂RN Omega subset {{mathbb{R}}}^{N} is a bounded smooth domain or the whole space RN {{mathbb{R}}}^{N} . Our results cover the borderline case p=1 p=1 , the Hilbert case p=2 p=2 , N>2s Ngt 2s , and the so-called Sobolev limiting case N=1 N=1 , s=12
建立了分数阶次临界Sobolev嵌入w0 s, p (Ω)“L q”(Ω)， {w} ＿ {0} ＿ {s,p} (Omega) hspace{0.33em}hookrightarrow＾hspace{0.33em}{L} q {（}Omega)的最佳常数的精细界，其中N≥1 N ge 1,0 ＆lt;S ＆lt;1 0 lt s lt 1, p=1,2 p= 1,2,1≤q ＆lt;p s∗= N p N−sp 1 le q ltp{ ＿ }s{ ^ }{ast＝}frac{Np}{N-sp}，和Ω∧R N Omegasubset{{mathbb{R}}} ^ {n}是一个有界光滑域或整个空间R N {{mathbb{R}}} ^ {n}。我们的结果涵盖了边界情形p=1 p=1, Hilbert情形p=2 p=2, N ＆gt;2s N gt s，以及所谓的Sobolev极限情况N=1 N=1, s= 1 2s = frac{1}{2}, p=2 p=2，其中通过极限过程给出了一个尖锐渐近估计。应用所得结果证明了一类广泛的非局部偏微分方程解的存在性和不存在性。
Abstract This article studies the stability of a stationary solution to the three-dimensional Navier-Stokes equations in a bounded domain, where surface tension effects are taken into account. More precisely, this article considers the stability of equilibrium figure of uniformly rotating viscous incompressible fluid in R 3 {{mathbb{R}}}^{3} , which are rotationally symmetric about a certain axis. It is proved that this stability result can be obtained by the positivity of the second variation of the energy functional associated with the equation that determines an equilibrium figure, provided that initial data are close to an equilibrium state. The unique global solution is constructed in the L p {L}^{p} -in-time and L q {L}^{q} -in-space setting with ( p , q ) ∈ ( 2 , ∞ ) × ( 3 , ∞ ) left(p,q)in left(2,infty )times left(3,infty ) satisfying 2 / p + 3 / q < 1 2hspace{0.1em}text{/}p+3text{/}hspace{0.1em}qlt 1 , where the solution becomes real analytic, jointly in time and space. It is also proved that the solution converges exponentially to the equilibrium.
{"title":"Stability of stationary solutions to the three-dimensional Navier-Stokes equations with surface tension","authors":"Keiichi Watanabe","doi":"10.1515/anona-2022-0279","DOIUrl":"https://doi.org/10.1515/anona-2022-0279","url":null,"abstract":"Abstract This article studies the stability of a stationary solution to the three-dimensional Navier-Stokes equations in a bounded domain, where surface tension effects are taken into account. More precisely, this article considers the stability of equilibrium figure of uniformly rotating viscous incompressible fluid in R 3 {{mathbb{R}}}^{3} , which are rotationally symmetric about a certain axis. It is proved that this stability result can be obtained by the positivity of the second variation of the energy functional associated with the equation that determines an equilibrium figure, provided that initial data are close to an equilibrium state. The unique global solution is constructed in the L p {L}^{p} -in-time and L q {L}^{q} -in-space setting with ( p , q ) ∈ ( 2 , ∞ ) × ( 3 , ∞ ) left(p,q)in left(2,infty )times left(3,infty ) satisfying 2 / p + 3 / q < 1 2hspace{0.1em}text{/}p+3text{/}hspace{0.1em}qlt 1 , where the solution becomes real analytic, jointly in time and space. It is also proved that the solution converges exponentially to the equilibrium.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44851901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, we show continuity of commutators of Calderón-Zygmund operators [ b , T ] left[b,T] with BMO functions in generalized Orlicz-Morrey spaces M Φ , φ ( R n ) {M}^{Phi ,varphi }left({{mathbb{R}}}^{n}) . We give necessary and sufficient conditions for the boundedness of the genuine Calderón-Zygmund operators T T and for their commutators [ b , T ] left[b,T] on generalized Orlicz-Morrey spaces, respectively.
{"title":"Characterizations for the genuine Calderón-Zygmund operators and commutators on generalized Orlicz-Morrey spaces","authors":"V. Guliyev, Meriban N. Omarova, M. Ragusa","doi":"10.1515/anona-2022-0307","DOIUrl":"https://doi.org/10.1515/anona-2022-0307","url":null,"abstract":"Abstract In this article, we show continuity of commutators of Calderón-Zygmund operators [ b , T ] left[b,T] with BMO functions in generalized Orlicz-Morrey spaces M Φ , φ ( R n ) {M}^{Phi ,varphi }left({{mathbb{R}}}^{n}) . We give necessary and sufficient conditions for the boundedness of the genuine Calderón-Zygmund operators T T and for their commutators [ b , T ] left[b,T] on generalized Orlicz-Morrey spaces, respectively.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44624523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We are concerned with the incompressible limit of global-in-time strong solutions with arbitrary large initial velocity for the three-dimensional compressible viscoelastic equations. The incompressibility is achieved by the large value of the volume viscosity, which is different from the low Mach number limit. To obtain the uniform estimates, we establish the estimates for the potential part and the divergence-free part of the velocity. As the volume viscosity goes to infinity, the dispersion associated with the pressure waves tends to disappear, but the large volume viscosity provides a strong dissipation on the potential part of the velocity forcing the flow to be almost incompressible.
{"title":"Incompressible limit for compressible viscoelastic flows with large velocity","authors":"Xianpeng Hu, Yaobin Ou, Dehua Wang, Lu Yang","doi":"10.1515/anona-2022-0324","DOIUrl":"https://doi.org/10.1515/anona-2022-0324","url":null,"abstract":"Abstract We are concerned with the incompressible limit of global-in-time strong solutions with arbitrary large initial velocity for the three-dimensional compressible viscoelastic equations. The incompressibility is achieved by the large value of the volume viscosity, which is different from the low Mach number limit. To obtain the uniform estimates, we establish the estimates for the potential part and the divergence-free part of the velocity. As the volume viscosity goes to infinity, the dispersion associated with the pressure waves tends to disappear, but the large volume viscosity provides a strong dissipation on the potential part of the velocity forcing the flow to be almost incompressible.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42191352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, under some weaker assumptions on a > 0 agt 0 and f f , the authors aim to study the existence of nontrivial radial solutions and nonexistence of nontrivial solutions for the following Schrödinger-Poisson system with zero mass potential − Δ u + ϕ u = − a ∣ u ∣ p − 2 u + f ( u ) , x ∈ R 3 , − Δ ϕ = u 2 , x ∈ R 3 , left{begin{array}{ll}-Delta u+phi u=-a{| u| }^{p-2}u+fleft(u),& xin {{mathbb{R}}}^{3}, -Delta phi ={u}^{2},& xin {{mathbb{R}}}^{3},end{array}right. where p ∈ 2 , 12 5 pin left(2,frac{12}{5}right) . In particular, as a corollary for the following system: − Δ u + ϕ u = − ∣ u ∣ p − 2 u + ∣ u ∣ q − 2 u , x ∈ R 3 , − Δ ϕ = u 2 , x ∈ R 3 , left{begin{array}{ll}-Delta u+phi u=-{| u| }^{p-2}u+{| u| }^{q-2}u,& xin {{mathbb{R}}}^{3}, -Delta phi ={u}^{2},& xin {{mathbb{R}}}^{3},end{array}right. a sufficient and necessary condition is obtained on the existence of nontrivial radial solutions.
摘要本文在> 0 a gt 0和f f的一些较弱的假设下，研究了以下具有零质量势能的Schrödinger-Poisson系统- Δ u + φ u = - a∣u∣p - 2 u + f (u)， x∈R 3， - Δ φ = u 2, x∈R 3, left ｛begin{array}{ll}-Delta u+phi u=-a{| u| }^{p-2}u+fleft(u),& xin {{mathbb{R}}}^{3}, -Delta phi ={u}^{2},& xin {{mathbb{R}}}^{3},end{array}right的非平凡径向解的存在性和非平凡解的不存在性。式中p∈2,125 p inleft (2, frac{12}{5}right)。特别地，作为以下系统的推论:−Δ u + φ u =−∣u∣p−2 u +∣u∣q−2 u, x∈R 3，−Δ φ = u 2, x∈R 3, left ｛begin{array}{ll}-Delta u+phi u=-{| u| }^{p-2}u+{| u| }^{q-2}u,& xin {{mathbb{R}}}^{3}, -Delta phi ={u}^{2},& xin {{mathbb{R}}}^{3},end{array}right。得到了非平凡径向解存在的一个充要条件。
{"title":"Existence and nonexistence of nontrivial solutions for the Schrödinger-Poisson system with zero mass potential","authors":"Xiaoping Wang, Fulai Chen, Fangfang Liao","doi":"10.1515/anona-2022-0319","DOIUrl":"https://doi.org/10.1515/anona-2022-0319","url":null,"abstract":"Abstract In this article, under some weaker assumptions on a > 0 agt 0 and f f , the authors aim to study the existence of nontrivial radial solutions and nonexistence of nontrivial solutions for the following Schrödinger-Poisson system with zero mass potential − Δ u + ϕ u = − a ∣ u ∣ p − 2 u + f ( u ) , x ∈ R 3 , − Δ ϕ = u 2 , x ∈ R 3 , left{begin{array}{ll}-Delta u+phi u=-a{| u| }^{p-2}u+fleft(u),& xin {{mathbb{R}}}^{3}, -Delta phi ={u}^{2},& xin {{mathbb{R}}}^{3},end{array}right. where p ∈ 2 , 12 5 pin left(2,frac{12}{5}right) . In particular, as a corollary for the following system: − Δ u + ϕ u = − ∣ u ∣ p − 2 u + ∣ u ∣ q − 2 u , x ∈ R 3 , − Δ ϕ = u 2 , x ∈ R 3 , left{begin{array}{ll}-Delta u+phi u=-{| u| }^{p-2}u+{| u| }^{q-2}u,& xin {{mathbb{R}}}^{3}, -Delta phi ={u}^{2},& xin {{mathbb{R}}}^{3},end{array}right. a sufficient and necessary condition is obtained on the existence of nontrivial radial solutions.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46259460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We address a quasi-stationary fluid–structure interaction problem coupled with cell reactions and growth, which comes from the plaque formation during the stage of the atherosclerotic lesion in human arteries. The blood is modeled by the incompressible Navier-Stokes equation, while the motion of vessels is captured by a quasi-stationary equation of nonlinear elasticity. The growth happens when both cells in fluid and solid react, diffuse and transport across the interface, resulting in the accumulation of foam cells, which are exactly seen as the plaques. Via a fixed-point argument, we derive the local well-posedness of the nonlinear system, which is sustained by the analysis of decoupled linear systems.
{"title":"Short-time existence of a quasi-stationary fluid–structure interaction problem for plaque growth","authors":"Helmut Abels, Yadong Liu","doi":"10.1515/anona-2023-0101","DOIUrl":"https://doi.org/10.1515/anona-2023-0101","url":null,"abstract":"Abstract We address a quasi-stationary fluid–structure interaction problem coupled with cell reactions and growth, which comes from the plaque formation during the stage of the atherosclerotic lesion in human arteries. The blood is modeled by the incompressible Navier-Stokes equation, while the motion of vessels is captured by a quasi-stationary equation of nonlinear elasticity. The growth happens when both cells in fluid and solid react, diffuse and transport across the interface, resulting in the accumulation of foam cells, which are exactly seen as the plaques. Via a fixed-point argument, we derive the local well-posedness of the nonlinear system, which is sustained by the analysis of decoupled linear systems.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, we consider the following Choquard system in R N N ≥ 1 {{mathbb{R}}}^{N}Nge 1 − Δ u + u = 2 p p + q ( I α ∗ ∣ v ∣ q ) ∣ u ∣ p − 2 u , − Δ v + v = 2 q p + q ( I α ∗ ∣ u ∣ p ) ∣ v ∣ q − 2 v , u ( x ) → 0 , v ( x ) → 0 as ∣ x ∣ → ∞ , left{begin{array}{l}-Delta u+u=frac{2p}{p+q}({I}_{alpha }ast | v{| }^{q})| u{| }^{p-2}u, -Delta v+v=frac{2q}{p+q}({I}_{alpha }ast | u{| }^{p})| v{| }^{q-2}v, uleft(x)to 0,vleft(x)to 0hspace{1em}hspace{0.1em}text{as}hspace{0.1em}hspace{0.33em}| x| to infty ,end{array}right. where N + α N < p , q < N + α N − 2 frac{N+alpha }{N}lt p,qlt frac{N+alpha }{N-2} , 2 ∗ α {2}_{ast }^{alpha } denotes N + α N − 2 frac{N+alpha }{N-2} if N ≥ 3 Nge 3 and 2 ∗ α ≔ ∞ {2}_{ast }^{alpha }:= infty if N = 1 , 2 N=1,2 , I α {I}_{alpha } is a Riesz potential. By analyzing the asymptotic behavior of Riesz potential energy, we prove that minimal action sign-changing solutions have an odd symmetry with respect to the a hyperplane when α alpha is either close to 0 or close to N N . Our results can be regarded as a generalization of the results by Ruiz et al.
抽象在这个文章,我们认为《R N N≥1跟踪Choquard系统{{R mathbb {}}} ^ {N, N ge 1−Δu + u = 2 p p + q (Iα∗∣v∣q)∣你∣p−2,−Δv + v = 2 q p + q (Iα∗∣u∣p)∣v∣q−2 v, u (x)→0,v (x) x→0美国∣∣→∞,向左拐{开始{}{}- l阵 u + u =三角洲frac {2p} {p + q} ({I}{阿尔法的在的| v {|} q ^ {}) | u u ^ {p - 2},{|的 - Delta v + v = frac {2q} {p + q} ({I}{阿尔法的在的| u {|} p ^ {}) | v ^ {q-2}{|的v,剩下 u (x)到0,v 向左拐(x)到0 hspace {1em} hspace{0。1em} 短信美国{}hspace{0。1em} hspace x{0。33em} | |到 infty, end{阵列的好。哪里N +α< p, q < N +αN−2 frac {N + 阿尔法}{}中尉p, q frac {N + 阿尔法}{已经开始的,2∗的α{2}{在}^{阿尔法的denotes N +αN−2 frac {N + 阿尔法}{已经开始,如果N≥3 ge 3和2∗α≔∞的{2}{在}^{}:=阿尔法 infty如果N = 1, 2的N = 120,我α{}{阿尔法}是一个Riesz申请表。asymptotic社会行为》由analyzing Riesz潜在的能源,我们至少证明那个sign-changing解决方案有一个奇怪的动作和尊重《百万hyperplane symmetry当α阿尔法是要么接近0或接近N N。我们的建议可以作为鲁伊斯和艾尔的代言。
{"title":"Symmetry and nonsymmetry of minimal action sign-changing solutions for the Choquard system","authors":"Jianqing Chen, Qian Zhang","doi":"10.1515/anona-2022-0286","DOIUrl":"https://doi.org/10.1515/anona-2022-0286","url":null,"abstract":"Abstract In this article, we consider the following Choquard system in R N N ≥ 1 {{mathbb{R}}}^{N}Nge 1 − Δ u + u = 2 p p + q ( I α ∗ ∣ v ∣ q ) ∣ u ∣ p − 2 u , − Δ v + v = 2 q p + q ( I α ∗ ∣ u ∣ p ) ∣ v ∣ q − 2 v , u ( x ) → 0 , v ( x ) → 0 as ∣ x ∣ → ∞ , left{begin{array}{l}-Delta u+u=frac{2p}{p+q}({I}_{alpha }ast | v{| }^{q})| u{| }^{p-2}u, -Delta v+v=frac{2q}{p+q}({I}_{alpha }ast | u{| }^{p})| v{| }^{q-2}v, uleft(x)to 0,vleft(x)to 0hspace{1em}hspace{0.1em}text{as}hspace{0.1em}hspace{0.33em}| x| to infty ,end{array}right. where N + α N < p , q < N + α N − 2 frac{N+alpha }{N}lt p,qlt frac{N+alpha }{N-2} , 2 ∗ α {2}_{ast }^{alpha } denotes N + α N − 2 frac{N+alpha }{N-2} if N ≥ 3 Nge 3 and 2 ∗ α ≔ ∞ {2}_{ast }^{alpha }:= infty if N = 1 , 2 N=1,2 , I α {I}_{alpha } is a Riesz potential. By analyzing the asymptotic behavior of Riesz potential energy, we prove that minimal action sign-changing solutions have an odd symmetry with respect to the a hyperplane when α alpha is either close to 0 or close to N N . Our results can be regarded as a generalization of the results by Ruiz et al.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44885067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This article considers the Cauchy problem for compressible Euler system in R {bf{R}} with damping, in which the coefficient depends on the space variable. Assuming the initial density has a small perturbation around a constant state and both the small perturbation and the small initial velocity field are compact supported, finite-time blow-up result will be established. This result reveals the fact that if the space-dependent damping coefficient decays fast enough in the far field (belongs to L 1 ( R ) {L}^{1}left({bf{R}}) ), then the damping is non-effective to the long-time behavior of the solution.
{"title":"Blow-up for compressible Euler system with space-dependent damping in 1-D","authors":"Jinbo Geng, Ning-An Lai, Manwai Yuen, Jiang Zhou","doi":"10.1515/anona-2022-0304","DOIUrl":"https://doi.org/10.1515/anona-2022-0304","url":null,"abstract":"Abstract This article considers the Cauchy problem for compressible Euler system in R {bf{R}} with damping, in which the coefficient depends on the space variable. Assuming the initial density has a small perturbation around a constant state and both the small perturbation and the small initial velocity field are compact supported, finite-time blow-up result will be established. This result reveals the fact that if the space-dependent damping coefficient decays fast enough in the far field (belongs to L 1 ( R ) {L}^{1}left({bf{R}}) ), then the damping is non-effective to the long-time behavior of the solution.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42971196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Soraya Fareh, K. Akrout, A. Ghanmi, Dušan D. Repovš
Abstract In this article, we study certain critical Schrödinger-Kirchhoff-type systems involving the fractional p p -Laplace operator on a bounded domain. More precisely, using the properties of the associated functional energy on the Nehari manifold sets and exploiting the analysis of the fibering map, we establish the multiplicity of solutions for such systems.
{"title":"Multiplicity results for fractional Schrödinger-Kirchhoff systems involving critical nonlinearities","authors":"Soraya Fareh, K. Akrout, A. Ghanmi, Dušan D. Repovš","doi":"10.1515/anona-2022-0318","DOIUrl":"https://doi.org/10.1515/anona-2022-0318","url":null,"abstract":"Abstract In this article, we study certain critical Schrödinger-Kirchhoff-type systems involving the fractional p p -Laplace operator on a bounded domain. More precisely, using the properties of the associated functional energy on the Nehari manifold sets and exploiting the analysis of the fibering map, we establish the multiplicity of solutions for such systems.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42239069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In the present work, we find the Lie point symmetries of the Ricci flow on an n -dimensional manifold, and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics. We apply this method to retrieve the Lie point symmetries of the Einstein equations (seen as a “static” Ricci flow) and of some particular types of metrics of interest, such as, on warped products of manifolds. Finally, we use the symmetries found to obtain invariant solutions of the Ricci flow for the particular families of metrics considered.
{"title":"Symmetries of Ricci flows","authors":"Enrique López, Stylianos Dimas, Yuri Bozhkov","doi":"10.1515/anona-2023-0106","DOIUrl":"https://doi.org/10.1515/anona-2023-0106","url":null,"abstract":"Abstract In the present work, we find the Lie point symmetries of the Ricci flow on an n -dimensional manifold, and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics. We apply this method to retrieve the Lie point symmetries of the Einstein equations (seen as a “static” Ricci flow) and of some particular types of metrics of interest, such as, on warped products of manifolds. Finally, we use the symmetries found to obtain invariant solutions of the Ricci flow for the particular families of metrics considered.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135954347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：