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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

  • Czech description

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