We prove a C∞ version of Nekhoroshev theorem for time dependent Hamiltonians in Rd×Td. Precisely, we prove a result showing that for all times the energy of the system is bounded by a constant times ⟨t⟩ɛ. We apply the result to the dynamics of a charged particle in Td subject to a time dependent electromagnetic field.
{"title":"Bounds on the growth of energy for particles on the torus with unbounded time dependent perturbations","authors":"Dario Bambusi","doi":"10.1063/5.0196229","DOIUrl":"https://doi.org/10.1063/5.0196229","url":null,"abstract":"We prove a C∞ version of Nekhoroshev theorem for time dependent Hamiltonians in Rd×Td. Precisely, we prove a result showing that for all times the energy of the system is bounded by a constant times ⟨t⟩ɛ. We apply the result to the dynamics of a charged particle in Td subject to a time dependent electromagnetic field.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"85 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study a nonlinear partial differential equation describing the evolution of a foam drainage in one dimensional case which was proposed by Goldfarb et al. in 1988 in order to investigate the flow of liquid through channels (Plateau borders) and nodes (intersections of four channels) between the bubbles, driven by gravity and capillarity. Its mathematical studies so far are mainly restricted within numerical and particular solutions; as for mathematical analysis of it there are only a few. We prove that the free boundary problem for the foam drainage equation in the region below an interface to the bottom in a foam column admits a unique global-in-time classical solution by the standard classical mathematical method, the maximum principle. Moreover, the existence of its steady solution and its stability are shown.
{"title":"Classical solvability to the free boundary problem for a foam drainage equation. II. From the interface to the bottom","authors":"Atusi Tani, Marie Tani","doi":"10.1063/5.0155457","DOIUrl":"https://doi.org/10.1063/5.0155457","url":null,"abstract":"We study a nonlinear partial differential equation describing the evolution of a foam drainage in one dimensional case which was proposed by Goldfarb et al. in 1988 in order to investigate the flow of liquid through channels (Plateau borders) and nodes (intersections of four channels) between the bubbles, driven by gravity and capillarity. Its mathematical studies so far are mainly restricted within numerical and particular solutions; as for mathematical analysis of it there are only a few. We prove that the free boundary problem for the foam drainage equation in the region below an interface to the bottom in a foam column admits a unique global-in-time classical solution by the standard classical mathematical method, the maximum principle. Moreover, the existence of its steady solution and its stability are shown.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"64 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study a nonlinear partial differential equation describing the evolution of a foam drainage in one dimensional case which was proposed by Goldfarb et al. [Izv. Akad. Nauk SSSR Mekh. Ghidk. Gaza 2, 103–108 (1988)] in order to investigate the flow of liquid through channels (Plateau borders) and nodes (intersections of four channels) between the bubbles, driven by gravity and capillarity. Its mathematical studies so far are mainly restricted within numerical and particular solutions; as for mathematical analysis of it there are only a few. We prove that the free boundary problem for the foam drainage equation in the region from the top to the interface in a foam column admits a unique global-in-time classical solution by the standard classical mathematical method, the maximum principle and the comparison theorem. Moreover, the existence of its steady solution and its stability are discussed.
我们研究 Goldfarb 等人[Izv. Akad. Nauk SSSR Mekh. Ghidk. Gaza 2, 103-108 (1988)]提出的描述一维情况下泡沫排水演变的非线性偏微分方程，以研究液体在重力和毛细管作用下通过气泡之间的通道（高原边界）和节点（四个通道的交叉点）的流动。迄今为止，对它的数学研究主要局限于数值解和特定解；至于数学分析，则寥寥无几。我们通过标准经典数学方法、最大值原理和比较定理证明，泡沫排水方程在泡沫柱顶部到界面区域的自由边界问题有唯一的全局时间经典解。此外，还讨论了其稳定解的存在性及其稳定性。
{"title":"Classical solvability to the free boundary problem for a foam drainage equation. I. From the top to the interface","authors":"Atusi Tani, Marie Tani","doi":"10.1063/5.0155449","DOIUrl":"https://doi.org/10.1063/5.0155449","url":null,"abstract":"We study a nonlinear partial differential equation describing the evolution of a foam drainage in one dimensional case which was proposed by Goldfarb et al. [Izv. Akad. Nauk SSSR Mekh. Ghidk. Gaza 2, 103–108 (1988)] in order to investigate the flow of liquid through channels (Plateau borders) and nodes (intersections of four channels) between the bubbles, driven by gravity and capillarity. Its mathematical studies so far are mainly restricted within numerical and particular solutions; as for mathematical analysis of it there are only a few. We prove that the free boundary problem for the foam drainage equation in the region from the top to the interface in a foam column admits a unique global-in-time classical solution by the standard classical mathematical method, the maximum principle and the comparison theorem. Moreover, the existence of its steady solution and its stability are discussed.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"23 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We derive the next order correction to the Dirac exchange energy for the free electron gas in a box with zero boundary conditions in the thermodynamic limit. The correction is of the order of the surface area of the box, and comes from three different contributions: (i) a real-space boundary layer, (ii) a boundary-condition-induced small shift of Fermi momentum and bulk density, and (iii) a long-range electrostatic finite-size correction. Moreover we show that the local density approximation, in addition to capturing the bulk term exactly, also produces a correction of the correct order but not the correct size. Generalized gradient approximation (GGA) corrections are found to be capable of capturing the surface term exactly, provided the gradient enhancement factor satisfies a simple explicit integral constraint. For current GGAs such as B88 and Perdew, Burke and Ernzerhof we find that the new constraint is not satisfied and the size of the surface correction is overestimated by about ten percent. The new constraint might thus be of interest for the design of future exchange functionals.
{"title":"Next-order correction to the Dirac exchange energy of the free electron gas in the thermodynamic limit and generalized gradient approximations","authors":"Thiago Carvalho Corso, Gero Friesecke","doi":"10.1063/5.0152359","DOIUrl":"https://doi.org/10.1063/5.0152359","url":null,"abstract":"We derive the next order correction to the Dirac exchange energy for the free electron gas in a box with zero boundary conditions in the thermodynamic limit. The correction is of the order of the surface area of the box, and comes from three different contributions: (i) a real-space boundary layer, (ii) a boundary-condition-induced small shift of Fermi momentum and bulk density, and (iii) a long-range electrostatic finite-size correction. Moreover we show that the local density approximation, in addition to capturing the bulk term exactly, also produces a correction of the correct order but not the correct size. Generalized gradient approximation (GGA) corrections are found to be capable of capturing the surface term exactly, provided the gradient enhancement factor satisfies a simple explicit integral constraint. For current GGAs such as B88 and Perdew, Burke and Ernzerhof we find that the new constraint is not satisfied and the size of the surface correction is overestimated by about ten percent. The new constraint might thus be of interest for the design of future exchange functionals.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"539 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we investigate the uniqueness of blowup at singular points of the free boundary in the superconductivity problem. We provide a sufficient condition and demonstrate that this condition can be verified in certain special cases. The proof of the main results in this paper is primarily based on Weiss-type and Monneau-type monotonicity formulas, and is inspired by the recent paper [Chen et al. arXiv: 2204.11426v2 (2022)].
{"title":"Uniqueness of blowup at singular points for superconductivity problem","authors":"Lili Du, Xu Tang, Cong Wang","doi":"10.1063/5.0213622","DOIUrl":"https://doi.org/10.1063/5.0213622","url":null,"abstract":"In this paper, we investigate the uniqueness of blowup at singular points of the free boundary in the superconductivity problem. We provide a sufficient condition and demonstrate that this condition can be verified in certain special cases. The proof of the main results in this paper is primarily based on Weiss-type and Monneau-type monotonicity formulas, and is inspired by the recent paper [Chen et al. arXiv: 2204.11426v2 (2022)].","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Consider a finite connected graph denoted as G = (V, E). This study explores a generalized Chern-Simons Higgs model, characterized by the equation Δu=λeu(eu−1)2p+1+f, where Δ denotes the graph Laplacian, λ is a real number, p is a non-negative integer, and f is a function on V. Through the computation of the topological degree, this paper demonstrates the existence of a single solution for the model. Further analysis of the interplay between the topological degree and the critical group of an associated functional reveals the presence of multiple solutions. These findings extend the work of Li et al. [Calc. Var. 63, 81 (2024)] and Chao and Hou [J. Math. Anal. Appl. 519, 126787 (2023)].
考虑一个有限连通图，表示为 G = (V，E)。本研究探讨了一个广义的切尔恩-西蒙斯希格斯模型，该模型的方程Δu=λeu(eu-1)2p+1+f，其中Δ表示图的拉普拉奇，λ是实数，p是非负整数，f是 V 上的函数。通过计算拓扑度，本文证明了该模型存在单解。通过进一步分析拓扑度和相关函数临界群之间的相互作用，发现了多解的存在。这些发现扩展了 Li 等人 [Calc. Var. 63, 81 (2024)] 以及 Chao 和 Hou [J. Math. Anal. Appl. 519, 126787 (2023)] 的工作。
{"title":"Solutions to a generalized Chern–Simons Higgs model on finite graphs by topological degree","authors":"Songbo Hou, Wenjie Qiao","doi":"10.1063/5.0210421","DOIUrl":"https://doi.org/10.1063/5.0210421","url":null,"abstract":"Consider a finite connected graph denoted as G = (V, E). This study explores a generalized Chern-Simons Higgs model, characterized by the equation Δu=λeu(eu−1)2p+1+f, where Δ denotes the graph Laplacian, λ is a real number, p is a non-negative integer, and f is a function on V. Through the computation of the topological degree, this paper demonstrates the existence of a single solution for the model. Further analysis of the interplay between the topological degree and the critical group of an associated functional reveals the presence of multiple solutions. These findings extend the work of Li et al. [Calc. Var. 63, 81 (2024)] and Chao and Hou [J. Math. Anal. Appl. 519, 126787 (2023)].","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"35 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Quantum symmetry of graph C*-algebras has been studied, under the consideration of different formulations, in the past few years. It is already known that the compact quantum group (C(S1)∗C(S1)∗⋯∗C(S1)︸|E(Γ)|−times,Δ) [in short, *|E(Γ)|C(S1),Δ] always acts on a graph C*-algebra for a finite, connected, directed graph Γ in the category introduced by Joardar and Mandal, where |E(Γ)| ≔ number of edges in Γ. In this article, we show that for a certain class of graphs including Toeplitz algebra, quantum odd sphere, matrix algebra etc. the quantum symmetry of their associated graph C*-algebras remains *|E(Γ)|C(S1),Δ in the category as mentioned before. More precisely, if a finite, connected, directed graph Γ satisfies the following graph theoretic properties: (i) there does not exist any cycle of length ≥2 (ii) there exists a path of length (|V(Γ)| − 1) which consists all the vertices, where |V(Γ)| ≔ number of vertices in Γ (iii) given any two vertices (may not be distinct) there exists at most one edge joining them, then the universal object coincides with *|E(Γ)|C(S1),Δ. Furthermore, we have pointed out a few counter examples whenever the above assumptions are violated.
{"title":"Rigidity on quantum symmetry for a certain class of graph C*-algebras","authors":"Ujjal Karmakar, Arnab Mandal","doi":"10.1063/5.0177215","DOIUrl":"https://doi.org/10.1063/5.0177215","url":null,"abstract":"Quantum symmetry of graph C*-algebras has been studied, under the consideration of different formulations, in the past few years. It is already known that the compact quantum group (C(S1)∗C(S1)∗⋯∗C(S1)︸|E(Γ)|−times,Δ) [in short, *|E(Γ)|C(S1),Δ] always acts on a graph C*-algebra for a finite, connected, directed graph Γ in the category introduced by Joardar and Mandal, where |E(Γ)| ≔ number of edges in Γ. In this article, we show that for a certain class of graphs including Toeplitz algebra, quantum odd sphere, matrix algebra etc. the quantum symmetry of their associated graph C*-algebras remains *|E(Γ)|C(S1),Δ in the category as mentioned before. More precisely, if a finite, connected, directed graph Γ satisfies the following graph theoretic properties: (i) there does not exist any cycle of length ≥2 (ii) there exists a path of length (|V(Γ)| − 1) which consists all the vertices, where |V(Γ)| ≔ number of vertices in Γ (iii) given any two vertices (may not be distinct) there exists at most one edge joining them, then the universal object coincides with *|E(Γ)|C(S1),Δ. Furthermore, we have pointed out a few counter examples whenever the above assumptions are violated.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"47 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper considers the chemotaxis model with density-suppressed motility: ut = ∇·(φ(v)∇u) + ∇·(ψ(v)u∇v) + f(u), vt = Δv + wz, wt = −wz, wt = −wz, zt = Δz − z + u, x ∈ Ω, t > 0 under homogeneous Neumann boundary conditions in a smooth bounded domain Ω⊂R2. Given that the positive motility function φ(v) has the lower-upper bound, we can conclude that the system possesses a unique bounded classical solution. Moreover, it is proved that the global bounded solution (u, v, w, z) will converge to r/μ1α−1,v̄0+w̄0,0,r/μ1α−1 as t → ∞.
{"title":"Global asymptotic stability in a two-dimensional chemotaxis model arising from tumor invasion","authors":"Chun Wu","doi":"10.1063/5.0145255","DOIUrl":"https://doi.org/10.1063/5.0145255","url":null,"abstract":"This paper considers the chemotaxis model with density-suppressed motility: ut = ∇·(φ(v)∇u) + ∇·(ψ(v)u∇v) + f(u), vt = Δv + wz, wt = −wz, wt = −wz, zt = Δz − z + u, x ∈ Ω, t > 0 under homogeneous Neumann boundary conditions in a smooth bounded domain Ω⊂R2. Given that the positive motility function φ(v) has the lower-upper bound, we can conclude that the system possesses a unique bounded classical solution. Moreover, it is proved that the global bounded solution (u, v, w, z) will converge to r/μ1α−1,v̄0+w̄0,0,r/μ1α−1 as t → ∞.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"64 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we establish new regularity criteria for the three-dimensional (3D) viscous incompressible magnetohydrodynamic (MHD) equations. It is proved that if the solution of the MHD equations satisfies u3∈Lp(0,T;Lq(R3)),j3∈Lr(0,T;Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32<s≤∞ or u3∈Lp(0,T;Lq(R3)),w3∈Lr(0,T;Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32<s≤∞, then the regularity of the solution on (0, T), where u3, j3 and ω3 are the third component of velocity u, current density ∇ × b and vorticity ∇ × u, respectively. These results give new improvements of regularity theory of weak solutions.
本文为三维（3D）粘性不可压缩磁流体动力学（MHD）方程建立了新的正则性准则。研究证明，如果 MHD 方程的解满足 u3∈Lp(0,T;Lq(R3)),j3∈Lr(0,T；Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32<s≤∞ or u3∈Lp(0,T;Lq(R3)),w3∈Lr(0,T;Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32<s≤∞，那么解在（0，T）上的正则性，其中 u3、j3 和 ω3 分别是速度 u、电流密度 ∇ × b 和涡度 ∇ × u 的第三分量。这些结果对弱解的正则性理论有了新的改进。
{"title":"Improved regularity criteria for the MHD equations","authors":"Weihua Wang, Shixia Xu","doi":"10.1063/5.0179393","DOIUrl":"https://doi.org/10.1063/5.0179393","url":null,"abstract":"In this paper, we establish new regularity criteria for the three-dimensional (3D) viscous incompressible magnetohydrodynamic (MHD) equations. It is proved that if the solution of the MHD equations satisfies u3∈Lp(0,T;Lq(R3)),j3∈Lr(0,T;Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32&lt;s≤∞ or u3∈Lp(0,T;Lq(R3)),w3∈Lr(0,T;Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32&lt;s≤∞, then the regularity of the solution on (0, T), where u3, j3 and ω3 are the third component of velocity u, current density ∇ × b and vorticity ∇ × u, respectively. These results give new improvements of regularity theory of weak solutions.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"81 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, benefited some ideas of Wang [J. Geom. Anal. 33, 18 (2023)] and Dufera et al. [J. Math. Anal. Appl. 509, 126001 (2022)], we investigate persistence of spatial analyticity for solution of the higher order nonlinear dispersive equation with the initial data in modified Gevrey space. More precisely, using the contraction mapping principle, the bilinear estimate as well as approximate conservation law, we establish the persistence of the radius of spatial analyticity till some time δ. Then, given initial data that is analytic with fixed radius σ0, we obtain asymptotic lower bound σ(t)≥c|t|−12, for large time t ≥ δ. This result improves earlier ones in the literatures, such as Zhang et al. [Discrete Contin. Dyn. Syst. B 29, 937–970 (2024)], Huang–Wang [J. Differ. Equations 266, 5278–5317 (2019)], Liu–Wang [Nonlinear Differ. Equations Appl. 29, 57 (2022)], Wang [J. Geom. Anal. 33, 18 (2023)] and Selberg–Tesfahun [Ann. Henri Poincaré 18, 3553–3564 (2017)].
{"title":"New lower bounds on the radius of spatial analyticity for the higher order nonlinear dispersive equation on the real line","authors":"Zaiyun Zhang, Youjun Deng, Xinping Li","doi":"10.1063/5.0211479","DOIUrl":"https://doi.org/10.1063/5.0211479","url":null,"abstract":"In this paper, benefited some ideas of Wang [J. Geom. Anal. 33, 18 (2023)] and Dufera et al. [J. Math. Anal. Appl. 509, 126001 (2022)], we investigate persistence of spatial analyticity for solution of the higher order nonlinear dispersive equation with the initial data in modified Gevrey space. More precisely, using the contraction mapping principle, the bilinear estimate as well as approximate conservation law, we establish the persistence of the radius of spatial analyticity till some time δ. Then, given initial data that is analytic with fixed radius σ0, we obtain asymptotic lower bound σ(t)≥c|t|−12, for large time t ≥ δ. This result improves earlier ones in the literatures, such as Zhang et al. [Discrete Contin. Dyn. Syst. B 29, 937–970 (2024)], Huang–Wang [J. Differ. Equations 266, 5278–5317 (2019)], Liu–Wang [Nonlinear Differ. Equations Appl. 29, 57 (2022)], Wang [J. Geom. Anal. 33, 18 (2023)] and Selberg–Tesfahun [Ann. Henri Poincaré 18, 3553–3564 (2017)].","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"219 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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