Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00542434" target="_blank" >RIV/67985840:_____/21:00542434 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1088/1361-6544/abe696" target="_blank" >https://doi.org/10.1088/1361-6544/abe696</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1361-6544/abe696" target="_blank" >10.1088/1361-6544/abe696</a>
Alternative languages
Result language
angličtina
Original language name
Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA19-04243S" target="_blank" >GA19-04243S: Partial differential equations in mechanics and thermodynamics of fluids</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Nonlinearity
ISSN
0951-7715
e-ISSN
1361-6544
Volume of the periodical
34
Issue of the periodical within the volume
4
Country of publishing house
GB - UNITED KINGDOM
Number of pages
29
Pages from-to
2659-2687
UT code for WoS article
000672932700001
EID of the result in the Scopus database
2-s2.0-85105086128