COLLISIONS IN THREE-DIMENSIONAL FLUID STRUCTURE INTERACTION PROBLEMS

被引：62

作者：

Hillairet, Matthieu ^{[1
]}

Takahashi, Takeo ^{[2
,3
]}

机构：

[1] Univ Toulouse 3, Lab MIP, IMT, F-31062 Toulouse 9, France

[2] Nancy Univ, CNRS, UMR 7502, Inst Elie Cartan,INRIA, F-54506 Vandoeuvre Les Nancy, France

[3] INRIA Nancy Grand Est, Team Project CORIDA, Villers Les Nancy, France

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2009年 / 40卷 / 06期

关键词：

fluid structure interactions; Cauchy theory; qualitative properties; collisions; INCOMPRESSIBLE VISCOUS-FLUID; RIGID-BODY; MOTION; WELLPOSEDNESS; BODIES; FLOW;

D O I：

10.1137/080716074

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with a system composed of a rigid ball moving into a viscous incompressible fluid over a fixed horizontal plane. The equations of motion for the fluid are the Navier-Stokes equations, and the equations for the motion of the rigid ball are obtained by applying Newton's laws. We show that for any weak solution of the corresponding system satisfying the energy inequality, the rigid ball never touches the plane. This result is the extension of that obtained in [M. Hillairet, Comm. Partial Differential Equations, 32 (2007), pp. 1345-1371] in the two-dimensional setting.

引用

页码：2451 / 2477

页数：27

共 15 条

[1]

[Anonymous], 1983, Problemes mathematiques en plasticite

[2] ON SLOW MOTION GENERATED IN A VISCOUS FLUID BY APPROACH OF A SPHERE TO A PLANE WALL OR STATIONARY SPHERE [J].

COOLEY, MDA ;

ONEILL, ME .

MATHEMATIKA, 1969, 16 (31P1) :37-&

[3] Wellposedness for the Navier-Stokes flow in the exterior of a rotating obstacle [J].

Cumsille, P ;

Tucsnak, M .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2006, 29 (05) :595-623

[4] WELLPOSEDNESS FOR THE SYSTEM MODELLING THE MOTION OF A RIGID BODY OF ARBITRARY FORM IN AN INCOMPRESSIBLE VISCOUS FLUID [J].

Cumsille, Patricio ;

Takahashi, Takeo .

CZECHOSLOVAK MATHEMATICAL JOURNAL, 2008, 58 (04) :961-992

[5] On the motion of rigid bodies in a viscous incompressible fluid [J].

Feireisl, E .

JOURNAL OF EVOLUTION EQUATIONS, 2003, 3 (03) :419-441

[6]

Fujita H., 1970, Journal of the Faculty of Science, University of Tokyo, Section 1A (Mathematics), V17, P403

[7]

GALDI GP, 1994, SPRINGER TRACTS NAT, V38

[8] Global Existence of Weak Solutions for Viscous Incompressible Flows around a Moving Rigid Body in Three Dimensions [J].

Gunzburger, Max D. ;

Lee, Hyung-Chun ;

Seregin, Gregory A. .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2000, 2 (03) :219-266

[9]

Hesla T.I., 2005, THESIS U MINNESOTA

[10] Lack of collision between solid bodies in a 2D incompressible viscous flow [J].

Hillairet, M. .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) :1345-1371

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