On the regularity of weak solutions to the fluid-rigid body interaction problem
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
On the regularity of weak solutions to the fluid-rigid body interaction problem
Original language description
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.
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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA22-01591S" target="_blank" >GA22-01591S: Mathematical theory and numerical analysis for equations of viscous newtonian compressible fluids</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematische Annalen
ISSN
0025-5831
e-ISSN
1432-1807
Volume of the periodical
389
Issue of the periodical within the volume
2
Country of publishing house
DE - GERMANY
Number of pages
46
Pages from-to
1007-1052
UT code for WoS article
001025874100001
EID of the result in the Scopus database
2-s2.0-85164137307