Volume 1, Issue 2
Self-Similar Solutions of Leray’s Type for Compressible Navier-Stokes Equations in Two Dimension

Xianpeng Hu

Commun. Math. Anal. Appl., 1 (2022), pp. 241-262.

Published online: 2022-03

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  • 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 $(\rho,\mathbf{u})=0.$

  • AMS Subject Headings

35A05, 76A10, 76D03

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COPYRIGHT: © Global Science Press

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

Hu , Xianpeng. (2022). Self-Similar Solutions of Leray’s Type for Compressible Navier-Stokes Equations in Two Dimension. Communications in Mathematical Analysis and Applications. 1 (2). 241-262. doi:10.4208/cmaa.2022-0001
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