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

黄丙远

doi:10.6054/j.jscnun.2017167

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

$\|\rho_0^\frac{1}{2}\mathbf{u}_0\|_{L^2}^2+\|\nabla\mathbf{d}_0\|_{L^2}^2 \varepsilon_0$ 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.

关键词:

整体存在性

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

$\|\rho_0^\frac{1}{2}\mathbf{u}_0\|_{L^2}^2+\|\nabla\mathbf{d}_0\|_{L^2}^2 \varepsilon_0$ is suitably small,and the global existence and uniqueness of the strong solutions are proved by energy method.

Keywords:

global existence

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期刊类型引用(2)

1.	刘楠，任永华，张建文. 二维不可压缩Navier-Stokes-Landau-Lifshitz方程组的全局强解. 应用数学. 2024(01): 148-158 . 百度学术
2.	刘新，张建文，任永华. 三维变密度不可压缩Navier-Stokes-Landau-Lifshitz方程组的整体强解. 纯粹数学与应用数学. 2024(03): 465-474 . 百度学术