二维不可压缩 Navier——Stokes——Landau——Lifshitz 方程组的整体强解

考虑了不可压缩 Navier--Stokes--Landau--Lifshitz 耦合模型在二维空间中的Cauchy 问题, 假设在初值密度满足$\rho_00$及初值能量具备$\|\rho_0^\frac{1}{2}\mathbf{u}_0\|_{L^2}^2+\|\nabla\mathbf{d}_0\|_{L^2}^2 \varepsilon_0$足够小的条件下, 利用能量方法证明了整体强解的存在唯一性.

Global Smooth Solutions for the 2D incompressibleNavier--Stokes--Landau--Lifshitz equations

The Cauchy problem for incompressible Navier--Stokes--Landau--Lifshitz equations in two-dimensional space is solved by the following assumptions:the initial density satisfies $\rho_00$,the initial energy $\|\rho_0^\frac{1}{2}\mathbf{u}_0\|_{L^2}^2+\|\nabla\mathbf{d}_0\|_{L^2}^2 \varepsilon_0$ is suitably small,and the global existence and uniqueness of the strong solutions are proved by energy method.