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Weak-strong uniqueness for the isentropic compressible Navier-Stokes system. (English) Zbl 1270.35342

From the summary: 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, 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.

MSC:

35Q30 Navier-Stokes equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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