Relative energy inequality and weak-strong uniqueness for an isothermal non-Newtonian compressible fluid

0574193 - MÚ 2024 RIV HR eng J - Journal Article
Andrášik, R. - Mácha, Václav - Vodák, R.
Relative energy inequality and weak-strong uniqueness for an isothermal non-Newtonian compressible fluid.
Glasnik Matematicki. Roč. 58, č. 1 (2023), s. 85-99. ISSN 0017-095X. E-ISSN 1846-7989
R&D Projects: GA ČR(CZ) GA22-01591S
Grant - others:AV ČR(CZ) AP2101
Program: Akademická prémie - Praemium Academiae
Institutional support: RVO:67985840
Keywords : compressible Navier-Stokes equations * non-constant viscosity * relative energy inequality * weak-strong uniqueness
OECD category: Pure mathematics
Impact factor: 0.4, year: 2022
Method of publishing: Limited access
https://doi.org/10.3336/gm.58.1.07

Our paper deals with three-dimensional nonsteady Navier-Stokes equations for non-Newtonian compressible fluids. It contains a derivation of the relative energy inequality for the weak solutions to these equations. We show that the standard energy inequality implies the relative energy inequality. Consequently, the relative energy inequality allows us to achieve a weak-strong uniqueness result. In other words, we present that the weak solution of the Navier-Stokes system coincides with the strong solution emanated from the same initial conditions as long as the strong solution exists. For this purpose, a new assumption on the co-ercivity of the viscous stress tensor was introduced along with two natural examples satisfying it.
Permanent Link: https://hdl.handle.net/11104/0344542