Well-Posedness for the 2D Non-Autonomous Incompressible Fluid Flow in Lipschitz-like Domain | Journal of Partial Differential Equations

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

Authors

Xin-Guang Yang Department of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
Shubin Wang School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

DOI:

https://doi.org/10.4208/jpde.v32.n1.6

Keywords:

Non-autonomous Navier-Stokes equation;Lipshitz-like domain;background flow function.

Abstract

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.

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Published

2019-04-12

Issue

Vol. 32 No. 1 (2019)

Section

Articles

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