不可压缩Navier-Stokes-Landau-Lifshitz方程组全局弱解的存在性
Existence of Global Weak Solution for the Incompressible Navier-Stokes-Landau-Lifshitz System
摘要: 本文在光滑有界区域中研究了二维不可压缩Navier-Stokes-Landau-Lifshitz方程组的初边值问题，在初始密度有正上下界(远离真空)并赋予齐次Dirichlet边界条件的框架下，利用推出的一个基本的能量不等式和Fadeo-Galerkin方法，得到了系统全局弱解的存在性。
Abstract: In this paper, the initial-boundary value problem of two-dimensional incompressible Navier-Stokes-Landau-Lifshitz equations is studied in smooth bounded regions. By the basic energy law and the Fadeo-Galerkin method, we prove the global existence of the weak solutions under the assumption that the initial density is strictly positive and bounded, and subject to homogeneous Dirichlet boundary conditions.
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