Weak-strong uniqueness for the compressible Navier-Stokes equations with a hard-sphere pressure law

0495258 - MÚ 2019 RIV CN eng J - Journal Article
Feireisl, Eduard - Lu, Y. - Novotný, A.
Weak-strong uniqueness for the compressible Navier-Stokes equations with a hard-sphere pressure law.
Science China Mathematics. Roč. 61, č. 11 (2018), s. 2003-2016. ISSN 1674-7283. E-ISSN 1869-1862
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : Navier-Stokes equations * hard-sphere pressure * weak-strong uniqueness
OECD category: Pure mathematics
Impact factor: 1.031, year: 2018
https://link.springer.com/article/10.1007%2Fs11425-017-9272-7

We consider the Navier-Stokes equations with a pressure function satisfying a hard-sphere law. That means the pressure, as a function of the density, becomes infinite when the density approaches a finite critical value. Under some structural constraints imposed on the pressure law, we show a weak-strong uniqueness principle in periodic spatial domains. The method is based on a modified relative entropy inequality for the system. The main difficulty is that the pressure potential associated with the internal energy of the system is largely dominated by the pressure itself in the area close to the critical density. As a result, several terms appearing in the relative energy inequality cannot be controlled by the total energy.
Permanent Link: http://hdl.handle.net/11104/0288260