Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation*Debayan Maity was partially supported by INSPIRE faculty fellowship (IFA18-MA128) and by Department of Atomic Energy, Government of India, under Project No. 12-R&D-TFR-5.01-0520. Arnab Roy was supported by the Czech Science Foundation (GAČR) Project GA19-04243S. The Institute of Mathematics, CAS is supported by RVO:67985840. Takéo Takahashi was partially supported by the ANR research Project IFSMACS (ANR-15-CE40-0010). (3rd March 2021)

• Record Type: Journal Article
• Authors: Maity, Debayan; Roy, Arnab; Takahashi, Takéo
• Is Part Of: Nonlinearity. Volume 34:Number 4(2021)
• Page Start: 2659
• Page End: 2687
• Publication Date: 2021-03-03
• Subjects: fluid–structure interaction -- compressible Navier–Stokes system -- strong solution -- existence and uniqueness -- wave equation; 35Q30 -- 35R37 -- 76N10; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/abe696
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this article, we consider a fluid–structure interaction system where the fluid is viscous and compressible and where the structure is a part of the boundary of the fluid domain and is deformable. The fluid is governed by the barotropic compressible Navier–Stokes system, whereas the structure displacement is described by a wave equation. We show that the corresponding coupled system admits a unique, strong solution for an initial fluid density and an initial fluid velocity in H 3 and for an initial deformation and an initial deformation velocity in H 4 and H 3 respectively. The reference configuration for the fluid domain is a rectangular cuboid with the elastic structure being the top face. We use a modified Lagrangian change of variables to transform the moving fluid domain into the rectangular cuboid and then analyze the corresponding linear system coupling a transport equation (for the density), a heat-type equation, and a wave equation. The corresponding results for this linear system and estimations of the coefficients coming from the change of variables allow us to perform a fixed point argument and to prove the existence and uniqueness of strong solutions for the nonlinear system, locally in time.