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arXiv · 2210.10878

On the exponential decay in time of solutions to a~generalized Navier-Stokes-Fourier system

Anna Abbatiello·Miroslav Bulíček·Petr Kaplický
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Abstract

We consider a non-Newtonian incompressible heat conducting fluid with prescribed nonuniform temperature on the boundary and with the no-slip boundary conditions for the velocity. We assume no external body forces. For the power-law like models with the power law index bigger than $11/5$ in three dimensions, we identify a class of solutions fulfilling the entropy equality and converging to the equilibria exponentially in a proper metric. In fact, we show the existence of a Lyapunov functional for the problem. Consequently, the steady solution is nonlinearly stable and attracts all suitable weak solutions.

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Anna Abbatiello, Miroslav Bulíček, Petr Kaplický. 2022-10-19. On the exponential decay in time of solutions to a~generalized Navier-Stokes-Fourier system. https://arxiv.org/abs/2210.10878

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