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

0548750 - MÚ 2022 RIV CH eng J - Článek v odborném periodiku
Al Baba, H. - Ghosh, Amrita - Muha, B. - Nečasová, Šárka
L-p-strong solution to fluid-rigid body interaction system with Navier slip boundary condition.
Journal of Elliptic and Parabolic Equations. Roč. 7, č. 2 (2021), s. 439-489. ISSN 2296-9020
Grant CEP: GA ČR(CZ) GA19-04243S
Institucionální podpora: RVO:67985840
Klíčová slova: fluid-structure interaction * rigid body * maximal regularity
Obor OECD: Pure mathematics
Způsob publikování: Omezený přístup
https://doi.org/10.1007/s41808-021-00134-9

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.
Trvalý link: http://hdl.handle.net/11104/0324817