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Measure-valued solutions to the complete Euler system. (English) Zbl 1408.35134

Summary: We introduce the concept of dissipative measure-valued solution to the complete Euler system describing the motion of an inviscid compressible fluid. These solutions are characterized by a parameterized (Young) measure and a dissipation defect in the total energy balance. The dissipation defect dominates the concentration errors in the equations satisfied by the Young measure. A dissipative measure-valued solution can be seen as the most general concept of solution to the Euler system retaining its structural stability. In particular, we show that a dissipative measure-valued solution necessarily coincides with a classical one on its life span provided they share the same initial data.

MSC:

35Q31 Euler equations
35L45 Initial value problems for first-order hyperbolic systems
76N15 Gas dynamics (general theory)
35R06 PDEs with measure
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