Mathematical analysis of the motion of a rigid body in a compressible Navier–Stokes–Fourier fluid. Issue 9 (20th May 2019)

• Record Type: Journal Article
• Authors: Haak, Bernhard H.; Maity, Debayan; Takahashi, Takéo; Tucsnak, Marius
• Is Part Of: Mathematische Nachrichten. Volume 292:Issue 9(2019)
• Page Start: 1972
• Page End: 2017
• Publication Date: 2019-05-20
• Subjects: compressible Navier–Stokes–Fourier system -- fluid‐particle interaction -- maximal regularity -- R‐sectorial operators -- strong solutions -- 35Q30 -- 76D05 -- 76N10; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201700425
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract: 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.