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

Autori
Al Baba, Hind ; Ghosh, Amrita ; Muha, Boris ; Nečasová, Šárka

Izvornik
Journal of Elliptic and Parabolic Equations (2296-9020) 7 (2021), 2; 439-489

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
fluid-rigid body system ; strong solutions ; maximal regularity ; non-Newtonian fluids

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA