Journal
JOURNAL OF MATHEMATICAL FLUID MECHANICS
Volume 14, Issue 4, Pages 717-730Publisher
SPRINGER BASEL AG
DOI: 10.1007/s00021-011-0091-9
Keywords
Suitable weak solution; Weak-strong uniqueness; Compressible Navier-Stokes system; Finite energy weak solution
Funding
- GA CR, Academy of Sciences of the Czech Republic [201/09/0917, AV0Z10190503]
- Basic Science Research Program through the National Research Foundation of Korea
- Ministry of Education, Science and Technology [2011-0007701]
- National Research Foundation of Korea [2011-0007701] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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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.
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