Regularity of weak solutions of the compressible isentropic Navier-Stokes equations

Desjardins, Benoît

Desjardins, Benoît (1997), Regularity of weak solutions of the compressible isentropic Navier-Stokes equations, Communications in Partial Differential Equations, 22, 5-6, p. 977-1008. http://dx.doi.org/10.1080/03605309708821291

Type

Article accepté pour publication ou publié

Date

1997

Journal name

Communications in Partial Differential Equations

Volume

Number

5-6

Publisher

Taylor & Francis

Pages

977-1008

Abstract (EN)

Regularity of weak solutions of the compressible isentropic Navier-Stokes equations is proven for small time in dimension N = 2 or 3 under periodic boundary conditions. In this paper, the initial density is not required to have a positive lower bound and the pressure law is assumed to satisfy a condition that reduces to τ > 1 when N = 2 and p() = aτ. Moreover,weak solutions in T2turn out to be smooth as long as the density remains bounded in L∞( T2).

Subjects / Keywords

Weak solutions; Navier–Stokes equations