Dynamics of several rigid bodies in a two-dimensional ideal fluid and convergence to vortex systems

Glass, Olivier; Sueur, Franck

hal.structure.identifier	CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.author	Glass, Olivier
hal.structure.identifier	Institut de Mathématiques de Bordeaux [IMB]
dc.contributor.author	Sueur, Franck HAL ID: 177864
dc.date.accessioned	2019-10-12T09:42:27Z
dc.date.available	2019-10-12T09:42:27Z
dc.date.issued	2019-10
dc.identifier.uri	https://basepub.dauphine.fr/handle/123456789/20102
dc.language.iso	en	en
dc.subject	rigid bodies	en
dc.subject	vortex system	en
dc.subject.ddc	515	en
dc.title	Dynamics of several rigid bodies in a two-dimensional ideal fluid and convergence to vortex systems	en
dc.type	Document de travail / Working paper
dc.description.abstracten	We consider the motion of several solids in a bounded cavity filled with a perfect incompressible fluid, in two dimensions. The solids move according to Newton's law, under the influence of the fluid's pressure, and the fluid dynamics is driven by the 2D incompressible Euler equations, which are set on the time-dependent domain corresponding to the cavity deprived of the sets occupied by the solids. We assume that the fluid vorticity is initially bounded and that the circulations around the solids may be non-zero. The existence of a unique corresponding solution, \`a la Yudovich, to this system, up to a possible collision, is known. In this paper we identify the limit dynamics of the system when the radius of some of the solids converge to zero depending on how, for each body, the inertia is scaled with the radius. We obtain in the limit some point vortex systems for the solids converging to particles and a form of Newton's law for the solids that have a fixed radius; for the fluid we obtain an Euler-type system. This extends earlier works to the case of several moving rigid bodies. A crucial point is to understand the interaction, through the fluid, between small moving solids, and for that we use some normal forms of the ODEs driving the motion of the solids in two steps: first we use a normal form for the system coupling the time-evolution of all the solids to obtain a rough estimate of the acceleration of the bodies, then we turn to some normal forms that are specific to each small solid, with an appropriate modulation related to the influence of the other solids and of the fluid vorticity, to obtain some precise uniform a priori estimates of the velocities of the bodies, and then pass to the limit.	en
dc.publisher.name	Cahier de recherche CEREMADE, Université Paris-Dauphine	en
dc.publisher.city	Paris	en
dc.identifier.citationpages	75	en
dc.relation.ispartofseriestitle	Cahier de recherche CEREMADE, Université Paris-Dauphine	en
dc.subject.ddclabel	Analyse	en
dc.identifier.citationdate	2019
dc.description.ssrncandidate	non	en
dc.description.halcandidate	non	en
dc.description.readership	recherche	en
dc.description.audience	International	en
dc.date.updated	2019-10-12T09:26:42Z
hal.author.function	aut
hal.author.function	aut

Files in this item

Name:: 1910.03158.pdf
Size:: 847.6Kb
Format:: PDF

View/Open

This item appears in the following Collection(s)

CEREMADE : Publications

Show simple item record

Dynamics of several rigid bodies in a two-dimensional ideal fluid and convergence to vortex systems

Files in this item

This item appears in the following Collection(s)

Related items