Weak Solutions for Compressible Isentropic Navier–Stokes Equations in Dimensions Three

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1907-1945
Journal / PublicationArchive for Rational Mechanics and Analysis
Volume242
Issue number3
Online published15 Oct 2021
Publication statusPublished - Dec 2021

Abstract

Except a closed set Sc with zero parabolic Hausdorff measure, the weak limit (ρ, u) of approximate solutions is a renormalized weak solution with finite energy of three dimensional compressible Navier–Stokes equations for γ ∈ (6/5, 3/2] as constructed by Lions and Feireisl et al. in the Leray sense. The key novelty of the paper is the improved integrability of pressure by localization, which is based on the faster decay of the gradient of velocity and the higher integrability of the Riesz potentials of both density and momentum.