Abstract
We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a weak solution, such as the ones built up by Lions (Compressible Models, Oxford Science, Oxford, 1998), so that it is unique. It is of fundamental importance since uniqueness of these solutions is not known in general. We present two different methods, one using relative entropy, the other one using an improved Gronwall inequality due to the author; these two approaches yield complementary results. Known weak-strong uniqueness results are improved and classical uniqueness results for this equation follow naturally.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 137-146 |
| Number of pages | 10 |
| Journal | Journal of Mathematical Fluid Mechanics |
| Volume | 13 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 2011 |
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ASJC Scopus subject areas
- Applied Mathematics
- Mathematical Physics
- Computational Mathematics
- Condensed Matter Physics
Cite this
Weak-strong uniqueness for the isentropic compressible navier-stokes system. / Germain, Pierre.
In: Journal of Mathematical Fluid Mechanics, Vol. 13, No. 1, 03.2011, p. 137-146.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Weak-strong uniqueness for the isentropic compressible navier-stokes system
AU - Germain, Pierre
PY - 2011/3
Y1 - 2011/3
N2 - We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a weak solution, such as the ones built up by Lions (Compressible Models, Oxford Science, Oxford, 1998), so that it is unique. It is of fundamental importance since uniqueness of these solutions is not known in general. We present two different methods, one using relative entropy, the other one using an improved Gronwall inequality due to the author; these two approaches yield complementary results. Known weak-strong uniqueness results are improved and classical uniqueness results for this equation follow naturally.
AB - We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a weak solution, such as the ones built up by Lions (Compressible Models, Oxford Science, Oxford, 1998), so that it is unique. It is of fundamental importance since uniqueness of these solutions is not known in general. We present two different methods, one using relative entropy, the other one using an improved Gronwall inequality due to the author; these two approaches yield complementary results. Known weak-strong uniqueness results are improved and classical uniqueness results for this equation follow naturally.
UR - http://www.scopus.com/inward/record.url?scp=79960586686&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79960586686&partnerID=8YFLogxK
U2 - 10.1007/s00021-009-0006-1
DO - 10.1007/s00021-009-0006-1
M3 - Article
VL - 13
SP - 137
EP - 146
JO - Journal of Mathematical Fluid Mechanics
JF - Journal of Mathematical Fluid Mechanics
SN - 1422-6928
IS - 1
ER -