Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation
Abstract
In this article, we consider a fluidstructure 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 NavierStokes 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 heattype 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. *Debayan Maity was partially supported by INSPIRE faculty fellowship (IFA18MA128) and by Department of Atomic Energy, Government of India, under Project No. 12R&DTFR5.010520. Arnab Roy was supported by the Czech Science Foundation (GAČR) Project GA1904243S. The Institute of Mathematics, CAS is supported by RVO:67985840. Takéo Takahashi was partially supported by the ANR research Project IFSMACS (ANR15CE400010).
 Publication:

Nonlinearity
 Pub Date:
 April 2021
 DOI:
 10.1088/13616544/abe696
 arXiv:
 arXiv:2006.00488
 Bibcode:
 2021Nonli..34.2659M
 Keywords:

 fluidstructure interaction;
 compressible NavierStokes system;
 strong solution;
 existence and uniqueness;
 wave equation;
 35Q30;
 35R37;
 76N10;
 Mathematics  Analysis of PDEs
 EPrint:
 doi:10.1088/13616544/abe696