05/05/2022, 17:00 — 18:00 — Sala P3.10, Pavilhão de Matemática
Arnab Roy, Basque Center of Applied Mathematics, Bilbao, Spain
Existence of strong solutions for a compressible viscous fluid and a wave equation interaction system
In this talk, 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 reference configuration for the fluid domain is a rectangular cuboid with the elastic structure being the top face. 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, locally-in-time 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.
