Time-periodic solutions to the full Navier–Stokes–Fourier system with radiation on the boundary

Abstract

The Navier-Stokes-Fourier system is a well established model for describing the motion of viscous compressible heat-conducting fluids. We study the existence of time-periodic weak solutions and improve the result from [3] in the following sense: we extend the class of pressure functions (i.e. consider lower exponent γ) and include also the effect of radiation on the boundary.

On the motion of a compressible viscous fluid driven by time periodic inflow/outflow boundary conditions

“…Similar problems for compressible fluids have been addressed in [14], Axmann and Pokorný [3], and in [15]. In all cases the fluid is driven by a time periodic volume force that may be mathematically acceptable but physically less relevant.…”

Existence of Stationary Weak Solutions for Compressible Heat Conducting Flows

“…The steady flow of a compressible heat-conducting fluid in a bounded domain Ω ⊂ R N , N = 2 or 3, with sufficiently smooth boundary, can be described as follows div (̺u) = 0, (1) div (̺u ⊗ u)…”

“…Due to estimates constructed in [22] and [26] it was possible to prove existence of a weak time periodic solutions to system (1)-(3) in the paper [8]. The result has been generalized in [1] .…”

Time-Periodic Weak Solutions to Incompressible Generalized Newtonian Fluids

“…So far all the mentioned results concern time-periodic incompressible flows, however similar problems for compressible models have been addressed in e.g. [4,14,15].…”