Regularity of weak solutions of compressible isentropic self-gravitating fluid

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• 作者：Ling Zhao^a ; ^{zhling@jmu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Zhong Tan^b ; ^{ztan85@xmu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35Q30 ; 35B99 ; 35D10 ; 76N10
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：147
• 期：Complete
• 页码：274-290
• 全文大小：680 K

文摘

In this paper, the regularity of weak solutions to the three-dimensional compressible isentropic self-gravitating viscous fluids is considered in periodic domain. Inspired by the idea of Desjardins (1997) [3,4], we get the higher integrability of density ρ$\rho$, and we remove the additional assumption of 7663f025ea893714dfa2561cb1f4b6" title="Click to view the MathML source">ρ∈L^∞(0,T;L^q₀)$\rho \in L^{\infty }(0,T;L^{q_0})$ in the work of Choe and Jin (2003). Finally, we prove the supremum of the density is finite and the infimum of the density is positive in the domain (0,T)×T³$(0,T)\times {\mathbb{T}}^3$ for a positive time T$T$. Moreover, Moser type iteration scheme is used to obtain the 76dc24b0" title="Click to view the MathML source">L^∞$L^{\infty }$ norm estimate of the velocity.