Commun. Math. Anal. Appl., 1 (2022), pp. 241-262.
Published online: 2022-03
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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} }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 $(\rho,\mathbf{u})=0.$