Well-Posedness for the 2D Non-Autonomous Incompressible Fluid Flow in Lipschitz-like Domain

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Non-autonomous Navier-Stokes equation Lipshitz-like domain background flow function
• 年，卷（期）: 2019,（1）
• 页码范围: 77-92
• 页数: 16页
• 分类号: O175.27
• 语种: 英文
• DOI: 10.4208/jpde.v32.n1.6

摘要

This paper is concerned with the global well-posedness and regularity of weak solutions for the 2D non-autonomous incompressible Navier-Stokes equation with a inhomogeneous boundary condition in Lipschitz-like domain.Using the estimate for governing steady state equation and Hardy's inequality,the existence and regularity of global unique weak solution can be proved.Moreover,these results also hold for 2D Navier-Stokes equation with Rayleigh's friction and Navier-Stokes-Voigt flow,but invalid for three dimension.