L-p-strong solution to fluid-rigid body interaction system with Navier slip boundary condition

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00548750" target="_blank" >RIV/67985840:_____/21:00548750 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s41808-021-00134-9" target="_blank" >https://doi.org/10.1007/s41808-021-00134-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s41808-021-00134-9" target="_blank" >10.1007/s41808-021-00134-9</a>

Result language
angličtina
Original language name
L-p-strong solution to fluid-rigid body interaction system with Navier slip boundary condition
Original language description
We study a fluid-structure interaction problem describing movement of a rigid body inside a bounded domain filled by a viscous fluid. The fluid is modelled by the generalized incompressible Naiver–Stokes equations which include cases of Newtonian and non-Newtonian fluids. The fluid and the rigid body are coupled via the Navier slip boundary conditions and balance of forces at the fluid-rigid body interface. Our analysis also includes the case of the nonlinear slip condition. The main results assert the existence of strong solutions, in an Lp- Lq setting, globally in time, for small data in the Newtonian case, while existence of strong solutions in Lp-spaces, locally in time, is obtained for non-Newtonian case. The proof for the Newtonian fluid essentially uses the maximal regularity property of the associated linear system which is obtained by proving the R-sectoriality of the corresponding operator. The existence and regularity result for the general non-Newtonian fluid-solid system then relies upon the previous case. Moreover, we also prove the exponential stability of the system in the Newtonian case.
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
<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

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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