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Mathematical analysis of the motion of a rigid body in a compressible Navier–Stokes–Fourier fluid
Author(s) -
Haak Bernhard H.,
Maity Debayan,
Takahashi Takéo,
Tucsnak Marius
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700425
Subject(s) - compressibility , rigid body , perturbation (astronomy) , fourier transform , mathematical analysis , mathematics , fourier series , motion (physics) , boundary value problem , fourier analysis , solid body , classical mechanics , navier–stokes equations , physics , mechanics , quantum mechanics
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 L p ‐ L q 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.