量子Navier-Stokes-Landau-Lifshitz方程光滑解的爆破问题  

Blow-Up of the Smooth Solutions to the Quantum Navier-Stokes-Landau-Lifshitz Equations

作　　者：邱臻 王光武 Qiu Zhen;Wang Guangwu(School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006)

机构地区：[1]广州大学数学与信息科学学院,广州510006

出　　处：《数学物理学报（A辑）》2022年第4期1074-1088,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(11801107);广州市科技计划项目-市校(院)联合资助项目(202102010467)。

摘　　要：该文研究量子Navier-Stokes-Landau-Lifshitz(QNSLL)方程组在区域Ω?R^(n)(n=1,2)上光滑解的爆破问题,证明了QNSLL方程组在上半空间R_(+)^(n)、全空间R^(n)以及球形区域上的光滑解将在有限时间内爆破,其中上半空间R_(+)^(n)、全空间R^(n)上的局部光滑解的爆破时间依赖于边界条件,球形区域的局部光滑解的爆破时间则依赖于边界条件和初值条件.特别地,以上结论对NSLL方程组也成立.In this paper,we investigate the blow-up of the smooth solutions to the quantum Navier-Stokes-Landau-Lifshitz systems(QNSLL)in the domainsΩ?R^(n)(n=1,2).We prove that the smooth solutions to the QNSLL will blow up in finite time in the domains half-space R_(+)^(n),whole-space R^(n)and ball.The paper also shows that the blow-up time of the smooth solutions in half-space or whole-space only depends on boundary conditions,while the the blow-up time of the smooth solutions in the ball depends on initial data and boundary conditions.In particular,the above conclusions are also valid for NSLL systems.

关 键 词：最子Navier-Stokes-Landau-Lifshitz方程 局部光滑解 爆破时间 

分 类 号：O175.29[理学—数学]