Axisymmetric solutions of the Chaplygin gas for initial negative radial velocity  

作　　者：郭俐辉 盛万成 

机构地区：[1]Department of Mathematics,College of Sciences,Shanghai University [2]College of Mathematics and System Sciences,Xinjiang University

出　　处：《Journal of Shanghai University(English Edition)》2010年第5期380-386,共7页上海大学学报（英文版）

基　　金：Project supported by the Natural Science Foundation of China (Grant No.10671120);the Shanghai Leading Academic Discipline Project (Grant No.J50101)

摘　　要：In this paper, a three-parameter family of self-similar and weak solutions are constructed rigorously in two space dimensions for all positive time to the Euler equations with axisymmetric and radial negative initial velocity for the Chaplygin gas. Under the axisymmetry and self-similar assumptions, the equations are reduced to a system of three ordinary differential equations, from which we obtain structures of solutions besides their existence. The solutions exhibit some phenomena, such as formation and evolution of black hole, expansion and explosive expansion, in the evolution of universe.In this paper, a three-parameter family of self-similar and weak solutions are constructed rigorously in two space dimensions for all positive time to the Euler equations with axisymmetric and radial negative initial velocity for the Chaplygin gas. Under the axisymmetry and self-similar assumptions, the equations are reduced to a system of three ordinary differential equations, from which we obtain structures of solutions besides their existence. The solutions exhibit some phenomena, such as formation and evolution of black hole, expansion and explosive expansion, in the evolution of universe.

关 键 词：Chaplygin gas AXISYMMETRIC CONCENTRATION 

分 类 号：O354[理学—流体力学]