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 $(\rho,\mathbf{u})=0.$