Local Existence Of Shock Front Solution To Piston Problem Of 2-Dimensional Axi-symmetrical Relativistic Euler Equations

The paper is to prove the local existence of shock front solution to the piston prob-lem of 2-D axially-symmetric relativistic Euler equations.When the speed of the piston is a perturbation of constant, Firstly, proper transformations of variable are introduced to trans-form the originally problem into a 0-1 problem, then by the method of Taylor expansion, an N-ordered approximate solutions are constructed, and then by the energy estimate on the corresponding linearized problem and by the Newton’s iterative method, we finally prove the local existence of the shock front solution.In addition, the paper also proved that if the initial state of the piston velocity and gas are constant disturbances, existence and uniqueness of the relativistic Euler equations of one-dimensional integral piston classic problem of discontinuous solutions.