TY - JOUR
T1 - Well-Posedness for the 2D Non-Autonomous Incompressible Fluid Flow in Lipschitz-like Domain
AU - Yang , Xin-Guang
AU - Wang , Shubin
JO - Journal of Partial Differential Equations
VL - 1
SP - 77
EP - 92
PY - 2019
DA - 2019/04
SN - 32
DO - http://doi.org/10.4208/jpde.v32.n1.6
UR - https://global-sci.org/intro/article_detail/jpde/13124.html
KW - Non-autonomous Navier-Stokes equation
KW - Lipshitz-like domain
KW - background flow
function.
AB - <p>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.</p>