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

By Eduard Feireisl, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Emil Wiedemann. Calculus of Variations and Partial Differential Equations, 2015

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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.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e72671bf8c59a93f1907b94caaff106ebf5b9482