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On uniqueness of dissipative solutions to the isentropic Euler system. (English) Zbl 1428.35325

Summary: The dissipative solutions can be seen as a convenient generalization of the concept of weak solution to the isentropic Euler system. They can be seen as expectations of the Young measures associated to a suitable measure-valued solution of the problem. We show that dissipative solutions coincide with weak solutions starting from the same initial data on condition that: (i) the weak solution enjoys certain Besov regularity; (ii) the symmetric velocity gradient of the weak solution satisfies a one-sided Lipschitz bound.

MSC:

35Q31 Euler equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35D30 Weak solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
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