On solutions for a generalized Navier–Stokes–Fourier system fulfilling the entropy equality-Reference-Cited by-同舟云学术

On solutions for a generalized Navier–Stokes–Fourier system fulfilling the entropy equality

Published:2022-09-26 Issue:2236 Volume:380 Page:
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Abbatiello Anna¹^ORCID,Bulíček Miroslav²^ORCID,Kaplický Petr²^ORCID

Affiliation:

1. Department of Mathematics ‘G. Castelnuovo’, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Rome, Italy

2. Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Prague 8, Czech Republic

Abstract

We consider a flow of a non-Newtonian heat conducting incompressible fluid in a bounded domain subjected to the homogeneous Dirichlet boundary condition for the velocity field and the Dirichlet boundary condition for the temperature. In three dimensions, for a power-law index greater or equal to 11 / 5 , we show the existence of a solution fulfilling the entropy equality. The entropy equality can be formally deduced from the energy equality by renormalization. However, such a procedure can be justified by the DiPerna–Lions theory only for p > 5 / 2 . The main novelty is that we do not renormalize the temperature equation, but rather construct a solution which fulfils the entropy equality. This article is part of the theme issue ‘Non-smooth variational problems and applications’.

Funder

Grantová Agentura České Republiky

ERC

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2021.0351

Reference9 articles.

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4. On a Navier–Stokes–Fourier-like system capturing transitions between viscous and inviscid fluid regimes and between no-slip and perfect-slip boundary conditions

5. Unconditional finite amplitude stability of a fluid in a mechanically isolated vessel with spatially non-uniform wall temperature

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