Weak solutions to the full Navier-Stokes-Fourier system with slip boundary conditions in time dependent domains

TL;DR

This paper proves the global existence of weak solutions to the compressible Navier-Stokes-Fourier system with slip boundary conditions in moving domains, using penalization and weak formulation techniques.

Contribution

It introduces a novel approach to handle boundary behavior, viscosity, and pressure in the weak solutions of the system in time-dependent domains.

Findings

Established global-in-time existence of weak solutions.

Developed a penalization method for boundary and pressure.

Replaced the thermal energy equation with a weak inequality.

Abstract

We consider the compressible Navier-Stokes-Fourier system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. Assuming that the pressure can be decomposed into an elastic part and a thermal part, we prove global-in-time existence of weak solutions. Our approach is based on the penalization of the boundary behavior, viscosity, and the pressure in the weak formulation. Moreover, the thermal energy equation is in the weak formulation replaced by the thermal energy inequality complemented with the global total energy inequality. In the approximation scheme the thermal energy inequality is consider to be satisfied in the renormalized sense.