Geodesic
Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 961-992 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 35B30, 35Q30, 35R35, 76D03, 76D05
Keywords: Navier-Stokes equations; incompressible fluid; rigid bodies 
@article{CMJ_2008_58_4_a7,
     author = {Cumsille, Patricio and Takahashi, Tak\'eo},
     title = {Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid},
     journal = {Czechoslovak Mathematical Journal},
     pages = {961--992},
     year = {2008},
     volume = {58},
     number = {4},
     mrnumber = {2471160},
     zbl = {1174.35092},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a7/}
}
TY  - JOUR
AU  - Cumsille, Patricio
AU  - Takahashi, Takéo
TI  - Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid
JO  - Czechoslovak Mathematical Journal
PY  - 2008
SP  - 961
EP  - 992
VL  - 58
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a7/
LA  - en
ID  - CMJ_2008_58_4_a7
ER  - 
%0 Journal Article
%A Cumsille, Patricio
%A Takahashi, Takéo
%T Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid
%J Czechoslovak Mathematical Journal
%D 2008
%P 961-992
%V 58
%N 4
%U http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a7/
%G en
%F CMJ_2008_58_4_a7
Cumsille, Patricio; Takahashi, Takéo. Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 961-992. http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a7/