@Article{CMAA-1-241, author = {Hu , Xianpeng}, title = {Self-Similar Solutions of Leray’s Type for Compressible Navier-Stokes Equations in Two Dimension}, journal = {Communications in Mathematical Analysis and Applications}, year = {2022}, volume = {1}, number = {2}, pages = {241--262}, abstract = {
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 $(\rho,\mathbf{u})=0.$
}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2022-0001}, url = {http://global-sci.org/intro/article_detail/cmaa/20307.html} }