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

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.