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 ...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.展开更多
基金Project supported by the Natural Science Foundation of China (Grant No.10671120)the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘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.
