Large time behavior for a simplified 1D model of fluid-solid interaction

被引:46
作者
Vázquez, LJ [1 ]
Zuazua, E [1 ]
机构
[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain
关键词
fluid-solid interaction; one space dimension; burgers equations; self similarity; large time behavior;
D O I
10.1081/PDE-120024530
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this article we consider a simple model in one space dimension for the interaction between a fluid and a solid represented by a point mass. The fluid is governed by the viscous Burgers equation and the solid mass, which shares the velocity of the fluid, is accelerated by the difference of pressure at both sides of it. We describe the asymptotic behavior of solutions for integrable data using energy estimates and scaling techniques. We prove that the asymptotic profile of the fluid is a self-similar solution of the Burgers equation with an appropriate total mass, and we describe the parabolic trajectory of the point mass. We also prove that, asymptotically, the difference of pressure to both sides of the point mass vanishes.
引用
收藏
页码:1705 / 1738
页数:34
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