Journal of Differential Equations最新文献_第2页

Dynamics and integrability of polynomial vector fields on the n-dimensional sphere

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-03-26 DOI: 10.1016/j.jde.2025.113253

Supriyo Jana, Soumen Sarkar

{"title":"Dynamics and integrability of polynomial vector fields on the n-dimensional sphere","authors":"Supriyo Jana, Soumen Sarkar","doi":"10.1016/j.jde.2025.113253","DOIUrl":"10.1016/j.jde.2025.113253","url":null,"abstract":"<div><div>In this paper, we characterize arbitrary polynomial vector fields on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We establish a necessary and sufficient condition for a degree one vector field on the odd-dimensional sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span> to be Hamiltonian. Additionally, we classify polynomial vector fields on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> up to degree two that possess an invariant great <span><math><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-sphere. We present a class of completely integrable vector fields on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We found a sharp bound for the number of invariant meridian hyperplanes for a polynomial vector field on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. Furthermore, we compute the sharp bound for the number of invariant parallel hyperplanes for any polynomial vector field on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. Finally, we study homogeneous polynomial vector fields on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, providing a characterization of their invariant <span><math><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-spheres.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113253"},"PeriodicalIF":2.4,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705668","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}

引用次数: 0

Global well-posedness of non-resistive quantum MHD system

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-03-26 DOI: 10.1016/j.jde.2025.113255

Sinan Wang, Jianfeng Zhou

引用次数: 0

Stability analysis for two coupled second order evolution equations

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-03-26 DOI: 10.1016/j.jde.2025.113246

Jianghao Hao , Zhaobin Kuang , Zhuangyi Liu , Jiongmin Yong

引用次数: 0

Local exact controllability to the trajectories for the two-dimensional magnetohydrodynamic system with controls acting only on the velocity field

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-03-26 DOI: 10.1016/j.jde.2025.113237

Qiang Tao , Zheng-an Yao , Xuan Yin

引用次数: 0

Global long time uniform well-posedness of 3D incompressible Navier-Stokes equations under time-independent uniqueness condition

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-03-26 DOI: 10.1016/j.jde.2025.113254

Xinglong Feng , Yinnian He

{"title":"Global long time uniform well-posedness of 3D incompressible Navier-Stokes equations under time-independent uniqueness condition","authors":"Xinglong Feng , Yinnian He","doi":"10.1016/j.jde.2025.113254","DOIUrl":"10.1016/j.jde.2025.113254","url":null,"abstract":"<div><div>In this work, inspired by the uniqueness condition of the 3D steady incompressible Navier-Stokes equations, we present a time-independent uniqueness condition depending on <span><math><mo>(</mo><mi>ν</mi><mo>,</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>,</mo><mi>Ω</mi><mo>)</mo></math></span> with <span><math><msub><mrow><mi>f</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>=</mo><msub><mrow><mi>sup</mi></mrow><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></msub><mo>⁡</mo><msub><mrow><mo>‖</mo><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>‖</mo></mrow><mrow><mn>0</mn><mo>,</mo><mi>Ω</mi></mrow></msub></math></span> and consider the fully discrete Galerkin method for the 3D time-dependent incompressible Navier-Stokes equations in the infinite time interval <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>. Furthermore, we provide the long time uniform stability and convergence of the fully discrete Galerkin solution and obtain the global uniform well-posedness (or the existence, uniqueness and long time stability of the solution) of the 3D time-dependent incompressible Navier-Stokes equations under the time-independent uniqueness condition by use of the compact theorem and a new a priori estimate of the fully discrete Galerkin solution.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113254"},"PeriodicalIF":2.4,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705542","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}

引用次数: 0

On logarithmic double phase problems

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-03-26 DOI: 10.1016/j.jde.2025.113247

Rakesh Arora , Ángel Crespo-Blanco , Patrick Winkert

引用次数: 0

Dynamics of a periodic predator-prey reaction-diffusion system in heterogeneous environments

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-03-25 DOI: 10.1016/j.jde.2025.113252

Zhenrui Zhang, Jinfeng Wang

引用次数: 0

Effects of fast diffusion in the logistic equation with refuge

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-03-25 DOI: 10.1016/j.jde.2025.113261

V.K. Ramos , C.A. Santos , A. Suárez

引用次数: 0

Stability for inverse potential scattering with attenuation

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-03-24 DOI: 10.1016/j.jde.2025.113259

Rong Sun , Ganghua Yuan , Yue Zhao

{"title":"Stability for inverse potential scattering with attenuation","authors":"Rong Sun , Ganghua Yuan , Yue Zhao","doi":"10.1016/j.jde.2025.113259","DOIUrl":"10.1016/j.jde.2025.113259","url":null,"abstract":"<div><div>This paper is concerned with inverse potential scattering problem for Helmholtz equation with constant attenuation. We first derive a logarithmic stability estimate for determining the potential at a single wavenumber by point-source boundary measurements. The proof utilizes the construction of complex geometric optics (CGO) solutions. Further, given the multi-wavenumber data, we derive a stability estimate which consists of two parts: one part is a Lipschitz data discrepancy and the other part is a logarithmic stability. The latter decreases as the wavenumber increases, which exhibits the phenomenon of increasing stability. The proof employs the physical asymptotic behavior of the radiated field and the properties of the Radon transform. Moreover, as multi-wavenumber data is available, the proof does not resort to the commonly used unphysical CGO solutions. We trace the dependence of the upper bound of the stability estimate on the constant attenuation through an analysis of the resolvent estimates. Both of the stability estimates show exponential dependence on the attenuation coefficient, which illustrates the poor resolution of the inverse scattering with attenuation.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"431 ","pages":"Article 113259"},"PeriodicalIF":2.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683314","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}

引用次数: 0

Chaoticity of generic points for ergodic measures in hyperbolic systems and beyond

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-03-24 DOI: 10.1016/j.jde.2025.113236

Xiaobo Hou, Xueting Tian, Xutong Zhao

{"title":"Chaoticity of generic points for ergodic measures in hyperbolic systems and beyond","authors":"Xiaobo Hou, Xueting Tian, Xutong Zhao","doi":"10.1016/j.jde.2025.113236","DOIUrl":"10.1016/j.jde.2025.113236","url":null,"abstract":"<div><div>In this paper, we search the chaotic behavior in the set of generic points of ergodic measures (called the Birkhoff basin) and find several types of chaoticity stronger than Li-Yorke chaos. More precisely, we consider nonuniformly hyperbolic systems first. On one hand, the Birkhoff basin of every ergodic hyperbolic measure with positive metric entropy exhibits a type of distributional chaos property between DC1 and Li-Yorke chaos, called Banach DC1. On the other hand, the Birkhoff basin of every totally ergodic hyperbolic measure with nondegenerate support exhibits a type of distributional chaos property between DC1 and DC2, called almost DC1. For hyperbolic systems, the Birkhoff basin of every ergodic measure with nondegenerate support from an elementary part of an Axiom A system exhibits both almost DC1 and Banach DC1, and the Birkhoff basin of any trivial ergodic measure supported on some fixed point exhibits Banach DC1 but no almost DC1.</div><div>In this process, Katok's shadowing and horseshoe approximation motivate us to obtain two types of weak specification property as useful techniques to reach our results. Such weak specifications are also valid to symbolic systems like sofic subshifts and <em>β</em>-shifts, so we put them as abstract frameworks in the proof part. Compared with Chen-Tian's result <span><span>[1]</span></span> considering the ergodic measures whose Birkhoff basin has a distal pair, we need to overcome general ergodic measures without the assumption of a distal pair and overcome the nonuniform difficulties from the weak specification property.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113236"},"PeriodicalIF":2.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143681725","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}

引用次数: 0