Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid

Title:

Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid

Creator:

Cumsille, Patricio and Takahashi, Takéo

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:3b93e535-3db4-44c3-85a8-16863248b304
uuid:3b93e535-3db4-44c3-85a8-16863248b304

Subject:

Navier-Stokes equations, incompressible fluid, and rigid bodies

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper, we consider the interaction between a rigid body and an incompressible, homogeneous, viscous fluid. This fluid-solid system is assumed to fill the whole space $\Bbb R^d$, $d=2$ or $3$. The equations for the fluid are the classical Navier-Stokes equations whereas the motion of the rigid body is governed by the standard conservation laws of linear and angular momentum. The time variation of the fluid domain (due to the motion of the rigid body) is not known {\it a priori}, so we deal with a free boundary value problem. \endgraf We improve the known results by proving a complete wellposedness result: our main result yields a local in time existence and uniqueness of strong solutions for $d=2$ or $3$. Moreover, we prove that the solution is global in time for $d=2$ and also for $d=3$ if the data are small enough.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

961-992

Source:

Czechoslovak Mathematical Journal | 2008 Volume:58 | Number:4

Harvested from:

CDK

Metadata only:

false