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Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation
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SYSNO ASEP 0542434 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation Author(s) Maity, D. (IN)
Roy, Arnab (MU-W) SAI, ORCID, RID
Takahashi, T. (FR)Source Title Nonlinearity. - : Institute of Physics Publishing - ISSN 0951-7715
Roč. 34, č. 4 (2021), s. 2659-2687Number of pages 29 s. Language eng - English Country GB - United Kingdom Keywords compressible Navier-Stokes system ; existence and uniqueness ; fluid-structure interaction ; strong solution, wave equation Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA19-04243S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000672932700001 EID SCOPUS 85105086128 DOI 10.1088/1361-6544/abe696 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2022 Electronic address https://doi.org/10.1088/1361-6544/abe696
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