二维不可压缩 Navier--Stokes--Landau--Lifshitz 方程组的整体强解
Global Smooth Solutions for the 2D incompressibleNavier--Stokes--Landau--Lifshitz equations
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摘要: 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^\frac12\mathbfu_0\|_L^2^2+\|\nabla\mathbfd_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.Abstract: 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^\frac12\mathbfu_0\|_L^2^2+\|\nabla\mathbfd_0\|_L^2^2 \varepsilon_0 is suitably small,and the global existence and uniqueness of the strong solutions are proved by energy method.
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