Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation

0542434 - MÚ 2022 RIV GB eng J - Journal Article
Maity, D. - Roy, Arnab - Takahashi, T.
Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation.
Nonlinearity. Roč. 34, č. 4 (2021), s. 2659-2687. ISSN 0951-7715. E-ISSN 1361-6544
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : compressible Navier-Stokes system * existence and uniqueness * fluid-structure interaction * strong solution, wave equation
OECD category: Pure mathematics
Impact factor: 1.934, year: 2021
Method of publishing: Limited access
https://doi.org/10.1088/1361-6544/abe696

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 H3 and for an initial deformation and an initial deformation velocity in H4 and H3 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.
Permanent Link: http://hdl.handle.net/11104/0319843