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

Feireisl E, Gwiazda P, Swierczewska-Gwiazda A, Wiedemann E (2016)

Publication Type: Journal article

Publication year: 2016

Journal

Calculus of Variations and Partial Differential Equations Springer Verlag (Germany)

Book Volume: 55

Article Number: 141

Journal Issue: 6

DOI: 10.1007/s00526-016-1089-1

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.

Authors with CRIS profile

Emil Wiedemann

Involved external institutions

Academy of Sciences of the Czech Republic (ASCR) / Akademie věd České republiky (AVČR) CZ Czech Republic (CZ) University of Warsaw / Uniwersytet Warszawski PL Poland (PL) Gottfried Wilhelm Leibniz Universität Hannover DE Germany (DE)

How to cite

APA:

Feireisl, E., Gwiazda, P., Swierczewska-Gwiazda, A., & Wiedemann, E. (2016). Dissipative measure-valued solutions to the compressible Navier–Stokes system. Calculus of Variations and Partial Differential Equations, 55(6). https://doi.org/10.1007/s00526-016-1089-1

MLA:

Feireisl, Eduard, et al. "Dissipative measure-valued solutions to the compressible Navier–Stokes system." Calculus of Variations and Partial Differential Equations 55.6 (2016).

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