TY - JOUR
T1 - Self-Similar Solutions of Leray’s Type for Compressible Navier-Stokes Equations in Two Dimension
AU - Hu , Xianpeng
JO - Communications in Mathematical Analysis and Applications
VL - 2
SP - 241
EP - 262
PY - 2022
DA - 2022/03
SN - 1
DO - http://doi.org/10.4208/cmaa.2022-0001
UR - https://global-sci.org/intro/article_detail/cmaa/20307.html
KW - Navier-Stokes equations, self-similar solutions, compressible.
AB - We study the backward self-similar solution of Leray’s type for compressible Navier-Stokes equations in dimension two. The existence of weak solutions is established via a compactness argument with the help of an higher
integrability of density. Moreover, if the density belongs to $L^∞(\mathbb{R}^2)$ and the
velocity belongs to $L^2(\mathbb{R}^2),$ the solution is trivial; that is $(\rho,\mathbf{u})=0.$