Global Classical Solutions For The Initial Value Problem Of System Of Chaplygin Gas Dynamics

This paper deals with the global classical solutions of the initial value problem of system of Chaplygin gas dynamics.Chapter one is an introduction. First introduce the mathematical model of system of one-dimensional gas dynamics under the Lagrangian representation and the results of global classical solutions of the initial value problem of polytropic gas.Then intro-duce the background and definition of Chaplygin gas.In Chapter two prove the global classical solutions of the initial value problem of syetem of one-dimensional isentropic and non-isentropic Chaplygin gas dynamics under the Lagrangian representation.Note that system of Chaplygin gas dynamics in the Lagrangian Coordinates is linear strictly hyperbolic system, which can permit the solution is global.Then I prove thatτ(t, x) is strictly greater than 0 under certain con-ditions.In Chapter three I show the existence of global classical solutions of system of Chaplygin gas dynamics in the Euler coordinates by proving the transformation be-tween Lagrangian coordinates and Euler coordinate is a global diffeomorphism.