In this paper, we study the existence of pullback attractors and pullback exponential attractors for lattice dynamical system in time-dependent sequence space. First, we introduce a new sequence space with time-dependent variable exponents. Second, two abstract criteria (or sufficient conditions) about the existence of pullback attractors and pullback exponential attractors are established for infinite dimensional lattice dynamical systems on time-dependent spaces of infinite sequences. Finally, for making full use of the above-mentioned abstract criteria, we consider a second order lattice system with nonstandard growth nonlinearity, and then the existence of bi-space pullback attractors and pullback exponential attractors on a time-dependent Musielak–Orlicz space is obtained. In particular, we point out that these criteria and analytical skills can be utilized to deal with other lattice systems satisfying nonstandard growth conditions.
{"title":"Pullback exponential attractors for second-order lattice system with nonstandard growth condition","authors":"Jiangwei Zhang, Zhiming Liu, Jianhua Huang","doi":"10.1063/5.0117249","DOIUrl":"https://doi.org/10.1063/5.0117249","url":null,"abstract":"In this paper, we study the existence of pullback attractors and pullback exponential attractors for lattice dynamical system in time-dependent sequence space. First, we introduce a new sequence space with time-dependent variable exponents. Second, two abstract criteria (or sufficient conditions) about the existence of pullback attractors and pullback exponential attractors are established for infinite dimensional lattice dynamical systems on time-dependent spaces of infinite sequences. Finally, for making full use of the above-mentioned abstract criteria, we consider a second order lattice system with nonstandard growth nonlinearity, and then the existence of bi-space pullback attractors and pullback exponential attractors on a time-dependent Musielak–Orlicz space is obtained. In particular, we point out that these criteria and analytical skills can be utilized to deal with other lattice systems satisfying nonstandard growth conditions.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"44 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72533565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of this paper is to consider the effective dynamic behavior of a class of stochastic weakly damped wave equations with a fast oscillation under the non-Lipschitz condition. We show that the slow component converges to the solution of the corresponding average equation. The result presented here extends the existing results from the Lipschitz to non-Lipschitz condition, which is a much weaker condition with a wider range of applications.
{"title":"Effective dynamics for a class of stochastic weakly damped wave equation with a fast oscillation","authors":"Jin-Wei Zhao, B. Ge, Lu Liu","doi":"10.1063/5.0137730","DOIUrl":"https://doi.org/10.1063/5.0137730","url":null,"abstract":"The purpose of this paper is to consider the effective dynamic behavior of a class of stochastic weakly damped wave equations with a fast oscillation under the non-Lipschitz condition. We show that the slow component converges to the solution of the corresponding average equation. The result presented here extends the existing results from the Lipschitz to non-Lipschitz condition, which is a much weaker condition with a wider range of applications.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"58 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84564482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop a revised Riemann–Hilbert problem (RHP) to the Fokas–Lenells (FL) equation with a zero boundary condition, satisfying the normalization condition, and the potential of the FL equation is recovered from the asymptotic behavior of RHP when the spectral parameter goes to zero. Under the reflection-less situation, we consider the RHP with 2N simple poles and two Nth order poles, respectively, and obtain the explicit formulas of Nth order soliton and positon solutions. As applications, the first-order soliton, the second-order soliton, and positon are displayed. Additionally, the collisions of N solitons are studied, and the phase shift and space shift are displayed.
{"title":"Explicit Nth order solutions of Fokas–Lenells equation based on revised Riemann–Hilbert approach","authors":"Yongshuai Zhang, Deqin Qiu, Jingsong He","doi":"10.1063/5.0148086","DOIUrl":"https://doi.org/10.1063/5.0148086","url":null,"abstract":"We develop a revised Riemann–Hilbert problem (RHP) to the Fokas–Lenells (FL) equation with a zero boundary condition, satisfying the normalization condition, and the potential of the FL equation is recovered from the asymptotic behavior of RHP when the spectral parameter goes to zero. Under the reflection-less situation, we consider the RHP with 2N simple poles and two Nth order poles, respectively, and obtain the explicit formulas of Nth order soliton and positon solutions. As applications, the first-order soliton, the second-order soliton, and positon are displayed. Additionally, the collisions of N solitons are studied, and the phase shift and space shift are displayed.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"11 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90056237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is devoted to establishing the global regularity involving magnetic fields and partial components of the velocity for the 3D generalized magnetohydrodynamic equations with dissipation terms −(−Δ)αu and −(−Δ)βb. We assume 1≤α=β≤32 and prove that if b,u3∈Lw(0,T;Lq(R3)) with 2αw+3q≤3(2α−1)4+3(1−ϵ)4q, 3+ϵ2α−1
{"title":"A regularity criterion for the 3D generalized MHD system involving partial components","authors":"Jinhuan Wang, W. Tan, Yongsheng Nie","doi":"10.1063/5.0143742","DOIUrl":"https://doi.org/10.1063/5.0143742","url":null,"abstract":"This paper is devoted to establishing the global regularity involving magnetic fields and partial components of the velocity for the 3D generalized magnetohydrodynamic equations with dissipation terms −(−Δ)αu and −(−Δ)βb. We assume 1≤α=β≤32 and prove that if b,u3∈Lw(0,T;Lq(R3)) with 2αw+3q≤3(2α−1)4+3(1−ϵ)4q, 3+ϵ2α−1<q≤∞, and 0<ϵ≤13, then the local strong solution is smooth on [0, T].","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"51 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90991847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we are devoted to establishing a new regularity criterion of weak solutions to incompressible axisymmetric Boussinesq equations. More precisely, we prove that for a small ϵ > 0, if the angular component of velocity field uθ(t, r, z) satisfies sup0 0, which is independent of the initial data, then the weak solution (u, ρ) to 3D Boussinesq equations is regular in (0, T].
{"title":"A regularity criterion for the 3D axisymmetric Boussinesq equations with non-zero swirl","authors":"Peng Wang, Zhengguang Guo","doi":"10.1063/5.0125404","DOIUrl":"https://doi.org/10.1063/5.0125404","url":null,"abstract":"In this paper, we are devoted to establishing a new regularity criterion of weak solutions to incompressible axisymmetric Boussinesq equations. More precisely, we prove that for a small ϵ > 0, if the angular component of velocity field uθ(t, r, z) satisfies sup0<t<T‖zuθ‖L∞(Ωδ)≤ϵ, where Ωδ≔x1,x2,z∈R3|x12+x22<δ denotes a thin cylinder with infinite height and radius δ > 0, which is independent of the initial data, then the weak solution (u, ρ) to 3D Boussinesq equations is regular in (0, T].","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"30 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85551028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Newman–Penrose (NP) constants of massless spin-0 fields propagating in Minkowski spacetime are computed close to spatial and null infinity by means of Friedrich’s i0-cylinder. Assuming a certain regularity condition on the initial data ensuring that the field extends analytically to critical sets, it is shown that the NP constants at future I+ and past null infinity I− are independent of each other. In other words, the classical NP constants at I± stem from different parts of the initial data given on a Cauchy hypersurface. In contrast, it is shown that, using a slight generalization of the classical NP constants, the associated quantities (i0-cylinder NP constants) do not require the regularity condition being satisfied and give rise to conserved quantities at I± that are determined by the same piece of initial data, which, in turn, correspond to the terms controlling the regularity of the field. Additionally, it is shown how the conservation laws associated with the NP constants can be exploited to construct, in flat space, heuristic asymptotic-system expansions, which are sensitive to the logarithmic terms at the critical sets.
{"title":"Spin-0 fields and the NP-constants close to spatial infinity in Minkowski spacetime","authors":"E. Gasperín, R. Pinto","doi":"10.1063/5.0158746","DOIUrl":"https://doi.org/10.1063/5.0158746","url":null,"abstract":"Newman–Penrose (NP) constants of massless spin-0 fields propagating in Minkowski spacetime are computed close to spatial and null infinity by means of Friedrich’s i0-cylinder. Assuming a certain regularity condition on the initial data ensuring that the field extends analytically to critical sets, it is shown that the NP constants at future I+ and past null infinity I− are independent of each other. In other words, the classical NP constants at I± stem from different parts of the initial data given on a Cauchy hypersurface. In contrast, it is shown that, using a slight generalization of the classical NP constants, the associated quantities (i0-cylinder NP constants) do not require the regularity condition being satisfied and give rise to conserved quantities at I± that are determined by the same piece of initial data, which, in turn, correspond to the terms controlling the regularity of the field. Additionally, it is shown how the conservation laws associated with the NP constants can be exploited to construct, in flat space, heuristic asymptotic-system expansions, which are sensitive to the logarithmic terms at the critical sets.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"31 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84995901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is known that static traversable wormholes in Einstein gravity are supported by matter that violates null energy conditions (NEC). Essentially, such wormholes will be characterized by a central throat with anisotropic matter lining the throat that violates NEC. This, in turn, provides viable geometry for the wormhole to sustain. In 2018, Herrera [Phys. Rev. D 97, 044010 (2018)] introduced a new classification for spherically symmetric bodies called “complexity factor.” It was proposed that a spherically symmetric non-trivial geometry can be classified as complex or non-complex based on the nature of the inhomogeneity and anisotropy of the stress–energy tensors with only homogeneous and isotropic matter distribution leading to null complexity. Mathematically, there was also another way of obtaining zero complexity geometry. In this context, since static traversable wormholes, by default, are characterized by anisotropic and inhomogeneous matter stress tensors, the question we answer is whether it is possible to obtain zero complexity class of wormholes supported by exotic matter.
众所周知，爱因斯坦引力中的静态可穿越虫洞是由违反零能条件(NEC)的物质支持的。从本质上讲，这种虫洞的特征是一个中央喉道，各向异性物质衬在喉道上，违反了NEC。这反过来又为虫洞提供了可行的几何结构。2018年，埃雷拉[物理学家]Rev. D 97,044010(2018)]引入了球对称体的新分类，称为“复杂性因子”。根据应力-能量张量的非均匀性和各向异性的性质，提出了球对称非平凡几何可以分为复杂几何和非复杂几何，只有均匀和各向同性的物质分布导致零复杂度。在数学上，还有另一种方法可以获得零复杂度几何。在这种情况下，由于静态可穿越虫洞默认具有各向异性和非均匀物质应力张量的特征，因此我们要回答的问题是，是否有可能获得由外来物质支持的零复杂度虫洞。
{"title":"Complexity factor parameterization for traversable wormholes","authors":"S. Bhattacharya, Subhasis Nalui","doi":"10.1063/5.0148762","DOIUrl":"https://doi.org/10.1063/5.0148762","url":null,"abstract":"It is known that static traversable wormholes in Einstein gravity are supported by matter that violates null energy conditions (NEC). Essentially, such wormholes will be characterized by a central throat with anisotropic matter lining the throat that violates NEC. This, in turn, provides viable geometry for the wormhole to sustain. In 2018, Herrera [Phys. Rev. D 97, 044010 (2018)] introduced a new classification for spherically symmetric bodies called “complexity factor.” It was proposed that a spherically symmetric non-trivial geometry can be classified as complex or non-complex based on the nature of the inhomogeneity and anisotropy of the stress–energy tensors with only homogeneous and isotropic matter distribution leading to null complexity. Mathematically, there was also another way of obtaining zero complexity geometry. In this context, since static traversable wormholes, by default, are characterized by anisotropic and inhomogeneous matter stress tensors, the question we answer is whether it is possible to obtain zero complexity class of wormholes supported by exotic matter.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"37 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77338675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study flat bands of periodic graphs in a Euclidean space. These are infinitely degenerate eigenvalues of the corresponding adjacency matrix, with eigenvectors of compact support. We provide some optimal recipes to generate desired bands and some sufficient conditions for a graph to have flat bands, we characterize the set of flat bands whose eigenvectors occupy a single cell, and we compute the list of such bands for small cells. We next discuss the stability and rarity of flat bands in special cases. Additional folklore results are proved, and many questions are still open.
{"title":"Flat bands of periodic graphs","authors":"Mostafa Sabri, Pierre Youssef","doi":"10.1063/5.0156336","DOIUrl":"https://doi.org/10.1063/5.0156336","url":null,"abstract":"We study flat bands of periodic graphs in a Euclidean space. These are infinitely degenerate eigenvalues of the corresponding adjacency matrix, with eigenvectors of compact support. We provide some optimal recipes to generate desired bands and some sufficient conditions for a graph to have flat bands, we characterize the set of flat bands whose eigenvectors occupy a single cell, and we compute the list of such bands for small cells. We next discuss the stability and rarity of flat bands in special cases. Additional folklore results are proved, and many questions are still open.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"9 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83643610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Joaquim Brugu'es, Sonja Hohloch, Pau Mir, Eva Miranda
In this article, we introduce b-semitoric systems as a generalization of semitoric systems, specifically tailored for b-symplectic manifolds. The objective of this article is to furnish a collection of examples and investigate the distinctive characteristics of these systems. A b-semitoric system is a four-dimensional b-integrable system that satisfies certain conditions: one of its momentum map components is proper and generates an effective global S1-action and all singular points are non-degenerate and devoid of hyperbolic components. To illustrate this concept, we provide five examples of b-semitoric systems by modifying the coupled spin oscillator and the coupled angular momenta, and we also classify their singular points. Additionally, we describe the dynamics of these systems through the image of their respective momentum maps.
{"title":"Constructions of b-semitoric systems","authors":"Joaquim Brugu'es, Sonja Hohloch, Pau Mir, Eva Miranda","doi":"10.1063/5.0152551","DOIUrl":"https://doi.org/10.1063/5.0152551","url":null,"abstract":"In this article, we introduce b-semitoric systems as a generalization of semitoric systems, specifically tailored for b-symplectic manifolds. The objective of this article is to furnish a collection of examples and investigate the distinctive characteristics of these systems. A b-semitoric system is a four-dimensional b-integrable system that satisfies certain conditions: one of its momentum map components is proper and generates an effective global S1-action and all singular points are non-degenerate and devoid of hyperbolic components. To illustrate this concept, we provide five examples of b-semitoric systems by modifying the coupled spin oscillator and the coupled angular momenta, and we also classify their singular points. Additionally, we describe the dynamics of these systems through the image of their respective momentum maps.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"11 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75096328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present an algebraic approach to the description of bound states in the continuum (BICs) in finite systems with a discrete energy spectrum coupled to several decay channels. General estimations and bounds on the number of linearly independent BICs are derived. We show that the algebraic point of view provides straightforward and illustrative interpretations of typical well-known results, including the Friedrich–Wintgen mechanism and the Pavlov-Verevkin model. Pair-wise annihilation and repulsion of BICs in the energy–parameter space are discussed within generic two- and three-level models. An illustrative algebraic interpretation of such phenomena in Hilbert space is presented.
{"title":"Algebraic approach to annihilation and repulsion of bound states in the continuum in finite systems","authors":"N. Shubin","doi":"10.1063/5.0142892","DOIUrl":"https://doi.org/10.1063/5.0142892","url":null,"abstract":"We present an algebraic approach to the description of bound states in the continuum (BICs) in finite systems with a discrete energy spectrum coupled to several decay channels. General estimations and bounds on the number of linearly independent BICs are derived. We show that the algebraic point of view provides straightforward and illustrative interpretations of typical well-known results, including the Friedrich–Wintgen mechanism and the Pavlov-Verevkin model. Pair-wise annihilation and repulsion of BICs in the energy–parameter space are discussed within generic two- and three-level models. An illustrative algebraic interpretation of such phenomena in Hilbert space is presented.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"37 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82713162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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