以测量值为初始数据的半平面涡度方程

IF 1.8 1区数学 Q1 MATHEMATICS, APPLIED

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-07-01 DOI:10.1016/j.anihpc.2020.10.002

Ken Abe

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引用次数: 0

摘要

考虑了半平面上具有有限测度初始涡度的二维Navier-Stokes方程，该方程具有Dirichlet边界条件。研究了具有小纯点部分测度的关联涡度方程的局部适定性和具有小总变分测度的全局适定性。我们的构造是基于与Stokes方程相关的涡度方程的解算子的l1估计。

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The vorticity equations in a half plane with measures as initial data

We consider the two-dimensional Navier-Stokes equations subject to the Dirichlet boundary condition in a half plane for initial vorticity with finite measures. We study local well-posedness of the associated vorticity equations for measures with a small pure point part and global well-posedness for measures with a small total variation. Our construction is based on an $L^{1}$ -estimate of a solution operator for the vorticity equations associated with the Stokes equations.

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来源期刊

Annales De L Institut Henri Poincare-Analyse Non Lineaire 数学-应用数学

CiteScore

4.10

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Nonlinear Analysis section of the Annales de l''Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.