Mathematical analysis of the motion of a rigid body in a compressible Navier–Stokes–Fourier fluid.

Haak, Bernhard H.; Maity, Debayan; Takahashi, Takéo; Tucsnak, Marius

We study an initial and boundary value problem modelling the motion of a rigid body in a heat conducting gas. The solid is supposed to be a perfect thermal insulator. The gas is described by the compressible Navier–Stokes–Fourier equations, whereas the motion of the solid is governed by Newton's laws. The main results assert the existence of strong solutions, in an Lp‐Lq setting, both locally in time and globally in time for small data. The proof is essentially using the maximal regularity property of associated linear systems. This property is checked by proving the R‐sectoriality of the corresponding operators, which in turn is obtained by a perturbation method.

MATHEMATICAL analysis; MOTION analysis; RIGID bodies; BOUNDARY value problems; INITIAL value problems; BODY temperature

Mathematische Nachrichten, 2019, Vol 292, Issue 9, p1972

0025-584X

Academic Journal

10.1002/mana.201700425