Relative Entropies, Suitable Weak Solutions, and Weak-Strong Uniqueness for the Compressible Navier–Stokes System

We introduce the notion of relative entropy for the weak solutions to the compressible Navier–Stokes system. In particular, we show that any finite energy weak solution satisfies a relative entropy inequality with respect to any couple of smooth functions satisfying relevant boundary conditions. As...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical fluid mechanics Vol. 14; no. 4; pp. 717 - 730
Main Authors Feireisl, Eduard, Jin, Bum Ja, Novotný, Antonín
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.12.2012
Springer Verlag
Subjects
Analysis of PDEs
Classical and Continuum Physics
Fluid- and Aerodynamics
Mathematical Methods in Physics
Mathematics
Physics
Physics and Astronomy
35D30
Compressible Navier–Stokes system
Finite energy weak solution
Suitable weak solution
Weak-strong uniqueness
76N10
Online AccessGet full text

Cover

More Information
Summary:We introduce the notion of relative entropy for the weak solutions to the compressible Navier–Stokes system. In particular, we show that any finite energy weak solution satisfies a relative entropy inequality with respect to any couple of smooth functions satisfying relevant boundary conditions. As a corollary, we establish the weak-strong uniqueness property in the class of finite energy weak solutions, extending thus the classical result of Prodi and Serrin to the class of compressible fluid flows.
ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-011-0091-9