WELL-POSEDNESS FOR A ONE-DIMENSIONAL FLUID-PARTICLE INTERACTION MODEL

被引：9

作者：

Andreianov, Boris ^{[1
,2
]}

Lagoutiere, Frederic ^{[3
]}

Seguin, Nicolas ^{[4
,5
,6
]}

Takahashi, Takeo ^{[7
,8
,9
]}

机构：

[1] Univ Franche Comte, CNRS, UMR 6623, Lab Math, F-25030 Besancon, France

[2] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

[3] Univ Paris 11, CNRS, UMR 8628, Lab Math, F-91405 Orsay, France

[4] Univ Paris 06, Sorbonne Univ, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France

[5] CNRS, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France

[6] INRIA Paris Rocquencourt, EPC Ange, F-78153 Le Chesnay, France

[7] Inria, F-54600 Villers Les Nancy, France

[8] Univ Lorraine, IECL, UMR 7502, F-54506 Vandoeuvre Les Nancy, France

[9] CNRS, IECL, UMR 7502, F-54506 Vandoeuvre Les Nancy, France

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2014年 / 46卷 / 02期

关键词：

fluid-particle interaction; Burgers equation; nonconservative coupling; well-posedness; BV estimates; wave-front tracking; splitting; fixed point; SCALAR CONSERVATION-LAWS; INVISCID FLUID; STRONG TRACES; COEFFICIENTS; CONVERGENCE; STABILITY; SYSTEMS;

D O I：

10.1137/130907963

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The fluid-particle interaction model introduced by the three last authors in [J. Differential Equations, 245 (2008), pp. 3503-3544] is the object of our study. This system consists of the Burgers equation with a singular source term (term that models the interaction via a drag force with a moving point particle) and of an ODE for the particle path. The notion of entropy solution for the singular Burgers equation is inspired by the theory of conservation laws with discontinuous flux developed by the first author, K. H. Karlsen, and N. H. Risebro in [Arch. Ration. Mech. Anal., 201 (2011), pp. 26-86]. In this paper, we prove well-posedness and justify an approximation strategy for the particle in Burgers system in the case of initial data of bounded variation. An existence result for L infinity data is also given.

引用

页码：1030 / 1052

页数：23

共 21 条

[1] ANALYSIS OF A BURGERS EQUATION WITH SINGULAR RESONANT SOURCE TERM AND CONVERGENCE OF WELL-BALANCED SCHEMES [J].

Andreianov, Boris ;

Seguin, Nicolas .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2012, 32 (06) :1939-1964

[2] A Theory of L 1-Dissipative Solvers for Scalar Conservation Laws with Discontinuous Flux [J].

Andreianov, Boris ;

Hvistendahl, Kenneth Karlsen ;

Risebro, Nils Henrik .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2011, 201 (01) :27-86

[3] SMALL SOLIDS IN AN INVISCID FLUID [J].

Andreianov, Boris ;

Lagoutiere, Frederic ;

Seguin, Nicolas ;

Takahashi, Takeo .

NETWORKS AND HETEROGENEOUS MEDIA, 2010, 5 (03) :385-404

[4]

[Anonymous], 2002, Applied Mathematical Sciences

[5] Mixed systems: ODEs - Balance laws [J].

Borsche, Raul ;

Colombo, Rinaldo M. ;

Garavello, Mauro .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (03) :2311-2338

[6] Kruzkov's estimates for scalar conservation laws revisited [J].

Bouchut, F ;

Perthame, B .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 350 (07) :2847-2870

[7] On the time continuity of entropy solutions [J].

Cances, Clement ;

Gallouet, Thierry .

JOURNAL OF EVOLUTION EQUATIONS, 2011, 11 (01) :43-55

[8] POLYGONAL APPROXIMATIONS OF SOLUTIONS OF INITIAL VALUE-PROBLEM FOR A CONSERVATION LAW [J].

DAFERMOS, CM .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1972, 38 (01) :33-&

[9] CONVERGENCE OF THE 2X2 GODUNOV METHOD FOR A GENERAL RESONANT NONLINEAR BALANCE LAW [J].

ISAACSON, E ;

TEMPLE, B .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1995, 55 (03) :625-640

[10] On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients [J].

Karlsen, KH ;

Risebro, NH .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2003, 9 (05) :1081-1104

← 1 2 3 →