Regularity of weak solutions of compressible isentropic self-gravitating fluid. (December 2016)

• Record Type: Journal Article
• Authors: Zhao, Ling; Tan, Zhong
• Is Part Of: Nonlinear analysis. Volume 147(2016)
• Page Start: 274
• Page End: 290
• Publication Date: 2016-12
• Subjects: 35Q30 -- 35B99 -- 35D10 -- 76N10; Compressible -- Regularity -- Weak solution; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.07.009
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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, and we remove the additional assumption of ρ ∈ L ∞ ( 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 ) × T 3 for a positive time T . Moreover, Moser type iteration scheme is used to obtain the L ∞ norm estimate of the velocity.