Optimal decay rates of isentropic compressible Navier-Stokes equations with discontinuous initial data

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)8132-8172
Journal / PublicationJournal of Differential Equations
Issue number10
Online published16 Jun 2020
Publication statusPublished - 5 Nov 2020


The global-in-time solutions with discontinuous initial data, when the density has no regularity, are constructed in [10–12] for the isentropic compressible Navier-Stokes equations in multi-dimensional spaces. The time decay rates of these solutions with low regularity still remain unsolved. In this paper we establish the decay rates of solutions in [10–12] in Lr-norm with 2≤r≤∞ and the decay rate of the first order derivative of the velocity in L2-norm when the initial data are bounded in L1. The optimal decay rates are also obtained. These decay rates are the same as rates for classical solutions in [18,20].

Research Area(s)

  • Discontinuous initial data, Large oscillations, Navier-Stokes equations, Optimal decay rates