Smooth solutions for the motion of a ball in an incompressible perfect fluid
type: Item
instance of: scholarly article
title: Smooth solutions for the motion of a ball in an incompressible perfect fluid
zbMATH Open document ID: 1173.35105
author: C. Rosier
author: Lionel Rosier
published in: Journal of Functional Analysis
publication date: 2009-04-08T00:00:00Z
review text: The authors consider the system of partial and ordinary differential equations which describes the motion of a rigid ball in the ideal fluid, i.e. the Euler incompressible equations, coupled with the system of ordinary differential equations describing the motion of the ball. In \(N\) space dimensions, provided the inital condition is sufficiently smooth, the authors show the existence of a smooth solution (with arbitrary smoothness if the data are so) to the studied system of differential equations. The proof is based on the abstract Kato-Lai theory from [\textit{T. Kato} and \textit{C. Y. Lai}, J. Funct. Anal. 56, 15--28 (1994; Zbl 0545.76007)]. The main difficulty is connected with the fact that a version of the Leray projection in domain changing with time has to be computed explicitely. If \(N=2\), the solution is global in time. The proof is based on a priori estimates relating the velocity to the vorticity in an exterior domain. The regularity of the solution is expressed in Sobolev spaces, without any weights.
reviewed by: Milan Pokorný
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76B03
Mathematics Subject Classification ID: 74F10
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 5541680
zbMATH Keywords: Euler equations
zbMATH Keywords: fluid-rigid body interaction
zbMATH Keywords: exterior domain
zbMATH Keywords: classical solutions
MaRDI profile type: Publication
full work available at URL: j.jfa.2008.10.024
OpenAlex ID: W2159138798
cites work: Q3438382
cites work: Remarks on the breakdown of smooth solutions for the 3-D Euler equations
cites work: Remarks on the Euler equation
cites work: On the detection of a moving obstacle in an ideal fluid by a boundary measurement
cites work: On the controllability of 2-D incompressible perfect fluids
cites work: Q4399897
cites work: Nonstationary flows of viscous and ideal fluids in \(R^3\)
cites work: Nonlinear evolution equations and the Euler flow
cites work: Q3666457
cites work: The existence and uniqueness of nonstationary ideal incompressible flow in exterior domains in \(R^ 3\)
cites work: Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid
cites work: On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid
cites work: On the Euler equations of incompressible perfect fluids
cites work: Q4127534
cites work: Q3689590
DOI: 10.1016/J.JFA.2008.10.024
description: scientific article; zbMATH DE number 5541680