TIME-PERIODIC WEAK SOLUTIONS FOR AN INCOMPRESSIBLE NEWTONIAN FLUID INTERACTING WITH AN ELASTIC PLATEast

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10456729" target="_blank" >RIV/00216208:11320/22:10456729 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Mb47n2Glw9" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Mb47n2Glw9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/21M1458946" target="_blank" >10.1137/21M1458946</a>

Result language
angličtina
Original language name
TIME-PERIODIC WEAK SOLUTIONS FOR AN INCOMPRESSIBLE NEWTONIAN FLUID INTERACTING WITH AN ELASTIC PLATEast
Original language description
Under the action of a time-periodic external force we prove the existence of at least one time-periodic weak solution for the interaction between a three-dimensional incompressible fluid, governed by the Navier-Stokes equation and a two-dimensional elastic plate. The challenge is that the Eulerian domain for the fluid changes in time and is a part of the solution. We introduce a two fixed-point methodology: First we construct a time-periodic solutions for a given variable time-periodic geometry. Then in a second step a (set-valued) fixed point is performed w.r.t. the geometry of the domain. The existence relies on newly developed a priori estimates applicable for both coupled and uncoupled variable geometries. Due to the expected weak regularity of the solutions such Eulerian estimates are unavoidable. Note in particular that only the fluid is assumed to be dissipative; the here-produced a priori estimates show that its possible to exploit the dissipative effects of the fluid also for the solid deformation. The existence of time-periodic solutions for a given geometry is valid for arbitrary large data. The existence of periodic coupled solutions to the fluid-structure interaction is valid for all data that exclude a self-intersection a priori.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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