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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM Journal on Mathematical Analysis

ISSN

0036-1410

e-ISSN

1095-7154

Svazek periodika

54

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

24

Strana od-do

4139-4162

Kód UT WoS článku

000841107900003

EID výsledku v databázi Scopus

2-s2.0-85135208292