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Large Time Behavior for a Simplified N-Dimensional Model of Fluid–Solid Interaction

dc.contributor.authorMunnier, Alexandre
HAL ID: 7734
dc.contributor.authorZuazua, Enrique
HAL ID: 10801
dc.date.accessioned2011-07-27T15:10:43Z
dc.date.available2011-07-27T15:10:43Z
dc.date.issued2005
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6820
dc.language.isoenen
dc.subjectFluid–solid interactionen
dc.subjectHeat kernelen
dc.subjectHeat-ODE coupled systemen
dc.subjectLarge time behavioren
dc.subjectSimilarity variablesen
dc.subject.ddc515en
dc.titleLarge Time Behavior for a Simplified N-Dimensional Model of Fluid–Solid Interactionen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper, we study the large time behavior of solutions of a parabolic equation coupled with an ordinary differential equation (ODE). This system can be seen as a simplified N-dimensional model for the interactive motion of a rigid body (a ball) immersed in a viscous fluid in which the pressure of the fluid is neglected. Consequently, the motion of the fluid is governed by the heat equation, and the standard conservation law of linear momentum determines the dynamics of the rigid body. In addition, the velocity of the fluid and that of the rigid body coincide on its boundary. The time variation of the ball position, and consequently of the domain occupied by the fluid, are not known a priori, so we deal with a free boundary problem. After proving the existence and uniqueness of a strong global in time solution, we get its decay rate in L p (1 ≤ p ≤ ∞), assuming the initial data to be integrable. Then, working in suitable weighted Sobolev spaces, and using the so-called similarity variables and scaling arguments, we compute the first term in the asymptotic development of solutions. We prove that the asymptotic profile of the fluid is the heat kernel with an appropriate total mass. The L ∞ estimates we get allow us to describe the asymptotic trajectory of the center of mass of the rigid body as well. We compute also the second term in the asymptotic development in L 2 under further regularity assumptions on the initial data.en
dc.relation.isversionofjnlnameCommunications in Partial Differential Equations
dc.relation.isversionofjnlvol30en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2005
dc.relation.isversionofjnlpages377-417en
dc.relation.isversionofdoihttp://dx.doi.org/10.1081/PDE-200050080en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherTaylor & Francisen
dc.subject.ddclabelAnalyseen


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