On the regularity of weak solutions to the fluid-rigid body interaction problem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00585942" target="_blank" >RIV/67985840:_____/24:00585942 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00208-023-02664-0" target="_blank" >https://doi.org/10.1007/s00208-023-02664-0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00208-023-02664-0" target="_blank" >10.1007/s00208-023-02664-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the regularity of weak solutions to the fluid-rigid body interaction problem

Popis výsledku v původním jazyce

We study a 3D fluid–rigid body interaction problem. The fluid flow is governed by 3D incompressible Navier–Stokes equations, while the motion of the rigid body is described by a system of ordinary differential equations describing conservation of linear and angular momentum. Our aim is to prove that any weak solution satisfying certain regularity conditions is smooth. This is a generalization of the classical result for the 3D incompressible Navier–Stokes equations, which says that a weak solution that additionally satisfy Prodi–Serrin Lr- Ls condition is smooth. We show that in the case of fluid–rigid body the Prodi–Serrin conditions imply W2,p and W1,p regularity for the fluid velocity and fluid pressure, respectively. Moreover, we show that solutions are C∞ if additionally we assume that the rigid body acceleration is bounded almost anywhere in time variable.

Název v anglickém jazyce

On the regularity of weak solutions to the fluid-rigid body interaction problem

Popis výsledku anglicky

We study a 3D fluid–rigid body interaction problem. The fluid flow is governed by 3D incompressible Navier–Stokes equations, while the motion of the rigid body is described by a system of ordinary differential equations describing conservation of linear and angular momentum. Our aim is to prove that any weak solution satisfying certain regularity conditions is smooth. This is a generalization of the classical result for the 3D incompressible Navier–Stokes equations, which says that a weak solution that additionally satisfy Prodi–Serrin Lr- Ls condition is smooth. We show that in the case of fluid–rigid body the Prodi–Serrin conditions imply W2,p and W1,p regularity for the fluid velocity and fluid pressure, respectively. Moreover, we show that solutions are C∞ if additionally we assume that the rigid body acceleration is bounded almost anywhere in time variable.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA22-01591S" target="_blank" >GA22-01591S: Matematická teorie a numerická analýza rovnic vazkých newtonovských stlačitelných tekutin</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Mathematische Annalen

ISSN

0025-5831

e-ISSN

1432-1807

Svazek periodika

389

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

46

Strana od-do

1007-1052

Kód UT WoS článku

001025874100001

EID výsledku v databázi Scopus

2-s2.0-85164137307