Relative Entropies, Suitable Weak Solutions, and Weak-Strong Uniqueness for the Compressible Navier–Stokes System

By Eduard Feireisl, Bum Ja Jin, Antonín Novotný. 2011

263 citations recorded by the source corpus.

We introduce the notion of relative entropy for the weak solutions to the compressible Navier–Stokes system. In particular, we show that any finite energy weak solution satisfies a relative entropy inequality with respect to any couple of smooth functions satisfying relevant boundary conditions. As a corollary, we establish the weak-strong uniqueness property in the class of finite energy weak solutions, extending thus the classical result of Prodi and Serrin to the class of compressible fluid flows.

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

View Paper: https://www.semanticscholar.org/paper/9ff2a24c152f2bba892c643031cc7200750806ea

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Antonín Novotný
2. Piotr Gwiazda
3. Eduard Feireisl
4. Julian Fischer
5. Agnieszka Świerczewska-Gwiazda
6. Emil Wiedemann
7. Didier Bresch
8. Franck Sueur

In Control and Systems Engineering

1. Antonín Novotný
2. Eduard Feireisl
3. Julian Fischer
4. Agnieszka Świerczewska-Gwiazda
5. Piotr Gwiazda
6. Emil Wiedemann
7. Franck Sueur
8. Didier Bresch

In Mathematical Physics

1. Piotr Gwiazda
2. Antonín Novotný
3. Julian Fischer
4. Eduard Feireisl
5. Agnieszka Świerczewska-Gwiazda
6. Emil Wiedemann
7. Franck Sueur
8. Xianpeng Hu

Citations in the corpus

• Dissipative measure-valued solutions to the compressible Navier–Stokes system (2015, background): “[10], Germain [15], Mellet and Vasseur [22], among others.”
• Weak–Strong Uniqueness Property for the Full Navier–Stokes–Fourier System (2011, methodology): “ system, unfortunately, in the class of “more regular” weak solutions which existence is not known, see also Desjardin [6] for the previous results in this direction. The problem is finally settled in [13] (see also [15]), where the weak-strong uniqueness is established in the class of the weak solut”
• Weak–strong uniqueness of solutions to entropy-dissipating reaction–diffusion equations (2017, background): “ENTROPY-DISSIPATING REACTION-DIFFUSION EQUATIONS 5 rely on relative entropies, for example the weak-strong uniqueness results for the compressible Navier-Stokes equation and related systems [16, 17].”
• On the Inviscid Limit for the Compressible Navier–Stokes System in an Impermeable Bounded Domain (2012, unknown): “Here, we will also get inspired by some recent breakthroughs in the issue of weak-strong uniqueness of the compressible Navier-Stokes equations, in particular by using some relative energy estimates recently proved by Feireisl, Ja Jin and Novotný in [14].”