期刊
JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS
卷 7, 期 2, 页码 439-489出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s41808-021-00134-9
关键词
Fluid-structure interaction; Rigid body; Maximal regularity; Generalized Navier-Stokes equations; Slip boundary condition
类别
资金
- Czech Science Foundation [GA19-04243S, RVO 67985840]
- Croatian Science Foundation (Hrvatska zaklada za znanost) [IP-2018-01-3706]
The study investigates fluid-structure interaction problem of a rigid body moving inside a viscous fluid, considering both Newtonian and non-Newtonian fluids. It establishes the existence and regularity of solutions, globally for small data in the Newtonian case and locally for non-Newtonian case, with proofs based on linear system properties and sectoriality of corresponding operator. The study also discusses the exponential stability of the system in the Newtonian case.
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 L-p- L-q setting, globally in time, for small data in the Newtonian case, while existence of strong solutions in L-p-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.
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