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arXiv · 1512.04852

Dissipative measure-valued solutions to the compressible Navier-Stokes system

Eduard Feireisl·Piotr Gwiazda·Agnieszka Świerczewska-Gwiazda·Emil Wiedemann
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Abstract

We introduce a new concept of dissipative measure-valued solution to the compressible Navier-Stokes system satisfying, in addition, a relevant form of the total energy balance. Then we show that a dissipative measure-valued and a standard smooth classical solution originating from the same initial data coincide (weak-strong uniqueness principle) as long as the latter exists. Such a result facilitates considerably the proof of convergence of solutions to various approximations including certain numerical schemes that are known to generate a measure-valued solution. As a byproduct we show that any measure-valued solution with bounded density component that starts from smooth initial data is necessarily a classical one.

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Eduard Feireisl, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Emil Wiedemann. 2015-12-15. Dissipative measure-valued solutions to the compressible Navier-Stokes system. https://arxiv.org/abs/1512.04852

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