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Journal of Mathematical Physics Analysis Geometry最新文献

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Explicit nondegeneracy conditions of KAM tori for the planar N-point vortex systems 平面n点涡旋系统KAM环面的显式非简并条件
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-06-01 DOI: 10.1063/5.0138452
Xuanqing Xiong, Qihuai Liu
{"title":"Explicit nondegeneracy conditions of KAM tori for the planar N-point vortex systems","authors":"Xuanqing Xiong, Qihuai Liu","doi":"10.1063/5.0138452","DOIUrl":"https://doi.org/10.1063/5.0138452","url":null,"abstract":"In this paper, we give an explicit nondegeneracy condition for the existence of Kolmogorov-Arnold-Moser (KAM) tori of an N-point vortex system on the plane by using the method of reduction via generalized Jacobi coordinates and matrix theory. Furthermore, by constructing a series of canonical transformations to reduce the degree of freedom of the Hamiltonian, we obtain a new simplified Hamiltonian system. Finally, we give the equivalent relationship between the relative equilibrium point of the original system and the equilibrium point of the new system.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"38 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83395313","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}
引用次数: 0
Generalized solutions to degenerate dynamical systems 退化动力系统的广义解
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-06-01 DOI: 10.1063/5.0144432
P. Jouan, U. Serres
{"title":"Generalized solutions to degenerate dynamical systems","authors":"P. Jouan, U. Serres","doi":"10.1063/5.0144432","DOIUrl":"https://doi.org/10.1063/5.0144432","url":null,"abstract":"The solutions to degenerate dynamical systems of the form A(x)ẋ=f(x) are studied by considering the equation as a differential inclusion. The set Z={det(A(x))=0}, called the singular set, is assumed to have an empty interior. The reasons leading us to the definition of the sets used for differential inclusion are exposed in detail. This definition is then applied on the one hand to generic cases and on the other hand to the particular cases resulting from physics, which can be found in Saavedra, Troncoso, and Zanelli [J. Math. Phys. 42, 4383 (2001)]. It is shown that generalized solutions may enter, leave, or remain in the singular locus.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"38 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79611467","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}
引用次数: 0
Cylindrical first-order superintegrability with complex magnetic fields 具有复磁场的圆柱一阶超可积性
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-06-01 DOI: 10.1063/5.0138095
O. Kubů, L. Šnobl
{"title":"Cylindrical first-order superintegrability with complex magnetic fields","authors":"O. Kubů, L. Šnobl","doi":"10.1063/5.0138095","DOIUrl":"https://doi.org/10.1063/5.0138095","url":null,"abstract":"This article is a contribution to the study of superintegrable Hamiltonian systems with magnetic fields on the three-dimensional Euclidean space E3 in quantum mechanics. In contrast to the growing interest in complex electromagnetic fields in the mathematical community following the experimental confirmation of its physical relevance [Peng et al., Phys. Rev. Lett. 114, 010601 (2015)], they were so far not addressed in the growing literature on superintegrability. Here, we venture into this field by searching for additional first-order integrals of motion to the integrable systems of cylindrical type. We find that already known systems can be extended into this realm by admitting complex coupling constants. In addition to them, we find one new system whose integrals of motion also feature complex constants. All these systems are multiseparable. Rigorous mathematical analysis of these systems is challenging due to the non-Hermitian setting and lost gauge invariance. We proceed formally and pose the resolution of these problems as an open challenge.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"40 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88479403","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}
引用次数: 1
Normalized ground states for fractional Kirchhoff equations with Sobolev critical exponent and mixed nonlinearities 具有Sobolev临界指数和混合非线性的分数阶Kirchhoff方程的归一化基态
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-06-01 DOI: 10.1063/5.0098126
L. Kong, Haibo Chen
{"title":"Normalized ground states for fractional Kirchhoff equations with Sobolev critical exponent and mixed nonlinearities","authors":"L. Kong, Haibo Chen","doi":"10.1063/5.0098126","DOIUrl":"https://doi.org/10.1063/5.0098126","url":null,"abstract":"In this paper, we study the existence of normalized ground states for nonlinear fractional Kirchhoff equations with Sobolev critical exponent and mixed nonlinearities in R3. To overcome the special difficulties created by the nonlocal term and fractional Sobolev critical term, we develop a perturbed Pohožaev method based on the Brézis–Lieb lemma and monotonicity trick. Using the Pohožaev manifold decomposition and fibering map, we prove the existence of a positive normalized ground state. Moreover, the asymptotic behavior of the obtained normalized solutions is also explored. These conclusions extend some known ones in previous papers.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"120 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90267594","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}
引用次数: 1
Large time behavior of weak solutions to the surface growth equation 表面生长方程弱解的大时间行为
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-06-01 DOI: 10.1063/5.0136559
Xuewen Wang, Chenggang Liu, Yanqing Wang, P. Han
{"title":"Large time behavior of weak solutions to the surface growth equation","authors":"Xuewen Wang, Chenggang Liu, Yanqing Wang, P. Han","doi":"10.1063/5.0136559","DOIUrl":"https://doi.org/10.1063/5.0136559","url":null,"abstract":"This paper studies the existence and decay estimates of weak solutions to the surface growth equation. First, the global existence of weak solutions is obtained by the approximation method introduced by Majda and Bertozzi [Vorticity and Incompressible Flow (Cambridge University Press, 2001)]. Then, we derive the L2-decay rates of weak solutions via the Fourier splitting method under the assumption that u0∈L1(R)∩L2(R). For more general cases, i.e., u0∈L2(R), the behavior of weak solutions in L2 is obtained by the spectral theory of self-adjoint operators.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"49 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74990965","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}
引用次数: 0
A new type restricted quantum group 一类新型受限量子群
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-06-01 DOI: 10.1063/5.0142193
Yongjun Xu, Jialei Chen
{"title":"A new type restricted quantum group","authors":"Yongjun Xu, Jialei Chen","doi":"10.1063/5.0142193","DOIUrl":"https://doi.org/10.1063/5.0142193","url":null,"abstract":"In this paper, we define a new type restricted quantum group Ūq(sl2*) and determine its Hopf Poincaré-Birkhoff-Witt-deformations Ūq(sl2*,κ) in which Ūq(sl2*,0)=Ūq(sl2*) and the classical restricted Drinfeld–Jimbo quantum group Ūq(sl2) is included. We show that Ūq(sl2*) is a basic Hopf algebra, then uniformly realize Ūq(sl2*) and Ūq(sl2) via some quotients of (deformed) preprojective algebras corresponding to the Gabriel quiver of Ūq(sl2*). Moreover, we obtain a uniform tensor-categorical realization of Ūq(sl2*) and Ūq(sl2), which is consistent with the above-mentioned Hopf-algebraic realization.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78501020","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}
引用次数: 1
Traveling waves in an evolving interstellar gas cloud 星际气体云中的行波
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-06-01 DOI: 10.1063/5.0127453
M. Humi
{"title":"Traveling waves in an evolving interstellar gas cloud","authors":"M. Humi","doi":"10.1063/5.0127453","DOIUrl":"https://doi.org/10.1063/5.0127453","url":null,"abstract":"This paper considers the possible emergence of traveling waves within an evolving interstellar gas cloud. To model this evolution, we use Euler–Poisson equations with the additional assumptions that the gas is incompressible, stratified, and self-gravitating. Within this framework, we establish that when the cloud has low density, the speed of these traveling waves is low. We suggest that the self-gravitational coalescence of embedded solid matter in the gas to form larger aggregates, such as cometary nuclei, may occur in the vicinity of wave crests where the mass density is highest. This idea is consistent with the widely agreed mechanism for planetary formation in proto-planetary disks, namely, that the accumulation of solids to form larger planetoids is initiated at the location of pressure maxima in the gas disk.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"08 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85978888","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}
引用次数: 0
The two-fluid incompressible Navier–Stokes–Maxwell system: Green’s function and optimal decay rate 双流体不可压缩Navier-Stokes-Maxwell系统:格林函数和最优衰减率
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-06-01 DOI: 10.1063/5.0132274
G. Wang, Mingying Zhong
{"title":"The two-fluid incompressible Navier–Stokes–Maxwell system: Green’s function and optimal decay rate","authors":"G. Wang, Mingying Zhong","doi":"10.1063/5.0132274","DOIUrl":"https://doi.org/10.1063/5.0132274","url":null,"abstract":"In this paper, we consider the two-fluid incompressible Navier–Stokes–Maxwell system in three dimensional space. The analysis shows that the effect of the Lorentz force induced by the electromagnetic field leads to some different structures of the spectrum. Moreover, the detailed analysis of the Green’s function to the linearized system is made with applications to derive the optimal time decay rate of the solution converging to the steady state.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"25 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80770320","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}
引用次数: 0
Decay rate to contact discontinuities for the one-dimensional compressible Navier–Stokes equations with a reacting mixture 具有反应混合物的一维可压缩Navier-Stokes方程的接触不连续衰减率
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-06-01 DOI: 10.1063/5.0104769
Lishuang Peng, Yong Li
{"title":"Decay rate to contact discontinuities for the one-dimensional compressible Navier–Stokes equations with a reacting mixture","authors":"Lishuang Peng, Yong Li","doi":"10.1063/5.0104769","DOIUrl":"https://doi.org/10.1063/5.0104769","url":null,"abstract":"In this paper, we investigate the nonlinear stability of contact waves for the Cauchy problem to the compressible Navier–Stokes equations for a reacting mixture in one dimension. If the corresponding Riemann problem for the compressible Euler system admits a contact discontinuity solution, it is shown that the contact wave is nonlinearly stable, while the strength of the contact discontinuity and the initial perturbation are suitably small. Especially, we obtain the convergence rate by using anti-derivative methods and elaborated energy estimates.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"30 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88409265","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}
引用次数: 1
Stability of the planar rarefaction wave to three-dimensional full compressible Navier–Stokes–Poisson system 平面稀疏波对三维全可压缩Navier-Stokes-Poisson系统的稳定性
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-06-01 DOI: 10.1063/5.0137502
Yeping Li, Yujuan Chen, Zhengzheng Chen
{"title":"Stability of the planar rarefaction wave to three-dimensional full\u0000 compressible Navier–Stokes–Poisson system","authors":"Yeping Li, Yujuan Chen, Zhengzheng Chen","doi":"10.1063/5.0137502","DOIUrl":"https://doi.org/10.1063/5.0137502","url":null,"abstract":"A full compressible Navier–Stokes–Poisson system models the motion of viscous ions under the effect of variable temperature and plays important roles in the study of self-gravitational viscous gaseous stars and in simulations of charged particles in semiconductor devices and plasmas physics. We establish the time-asymptotic nonlinear stability of a planar rarefaction wave to the initial value problem of a three-dimensional full compressible Navier–Stokes–Poisson equation when the initial data are a small perturbation of the planar rarefaction wave. The proof is given by a delicate energy method, which involves highly non-trivial a priori bounds due to the effect of the self-consistent electric field. This appears as the first result on the nonlinear stability of wave patterns to the full compressible Navier–Stokes–Poisson system in multi-dimensions.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"67 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76971956","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}
引用次数: 0
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