Smoothness of the motion of a rigid body immersed in an incompressible perfect fluid

Olivier Glass; Franck Sueur; Takéo Takahashi

Annales scientifiques de l'École Normale Supérieure (2012)

  • Volume: 45, Issue: 1, page 1-51
  • ISSN: 0012-9593

Abstract

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We consider the motion of a rigid body immersed in an incompressible perfect fluid which occupies a three-dimensional bounded domain. For such a system the Cauchy problem is well-posed locally in time if the initial velocity of the fluid is in the Hölder space C 1 , r . In this paper we prove that the smoothness of the motion of the rigid body may be only limited by the smoothness of the boundaries (of the body and of the domain). In particular for analytic boundaries the motion of the rigid body is analytic (till the classical solution exists and in particular till the solid does not hit the boundary). Moreover in this case this motion depends smoothly on the initial data.

How to cite

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Glass, Olivier, Sueur, Franck, and Takahashi, Takéo. "Smoothness of the motion of a rigid body immersed in an incompressible perfect fluid." Annales scientifiques de l'École Normale Supérieure 45.1 (2012): 1-51. <http://eudml.org/doc/272145>.

@article{Glass2012,
abstract = {We consider the motion of a rigid body immersed in an incompressible perfect fluid which occupies a three-dimensional bounded domain. For such a system the Cauchy problem is well-posed locally in time if the initial velocity of the fluid is in the Hölder space $C^\{1,r\}$. In this paper we prove that the smoothness of the motion of the rigid body may be only limited by the smoothness of the boundaries (of the body and of the domain). In particular for analytic boundaries the motion of the rigid body is analytic (till the classical solution exists and in particular till the solid does not hit the boundary). Moreover in this case this motion depends smoothly on the initial data.},
author = {Glass, Olivier, Sueur, Franck, Takahashi, Takéo},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {fluid-solid interaction; regularity properties; perfect incompressible fluid},
language = {eng},
number = {1},
pages = {1-51},
publisher = {Société mathématique de France},
title = {Smoothness of the motion of a rigid body immersed in an incompressible perfect fluid},
url = {http://eudml.org/doc/272145},
volume = {45},
year = {2012},
}

TY - JOUR
AU - Glass, Olivier
AU - Sueur, Franck
AU - Takahashi, Takéo
TI - Smoothness of the motion of a rigid body immersed in an incompressible perfect fluid
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2012
PB - Société mathématique de France
VL - 45
IS - 1
SP - 1
EP - 51
AB - We consider the motion of a rigid body immersed in an incompressible perfect fluid which occupies a three-dimensional bounded domain. For such a system the Cauchy problem is well-posed locally in time if the initial velocity of the fluid is in the Hölder space $C^{1,r}$. In this paper we prove that the smoothness of the motion of the rigid body may be only limited by the smoothness of the boundaries (of the body and of the domain). In particular for analytic boundaries the motion of the rigid body is analytic (till the classical solution exists and in particular till the solid does not hit the boundary). Moreover in this case this motion depends smoothly on the initial data.
LA - eng
KW - fluid-solid interaction; regularity properties; perfect incompressible fluid
UR - http://eudml.org/doc/272145
ER -

References

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