Original scientific paper

https://doi.org/10.3336/gm.58.1.07

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

Richard Andrášik ; Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic
Václav Mácha ; Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic
Rostislav Vodák orcid.org/0000-0003-1776-4050 ; Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic

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Abstract

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 coercivity of the viscous stress tensor was introduced along with two natural examples satisfying it.

Keywords

Compressible Navier-Stokes equations, non-constant viscosity, relative energy inequality, weak-strong uniqueness

Hrčak ID:

304393

URI

https://hrcak.srce.hr/304393

Publication date:

20.6.2023.

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