Global Entropy Solutions To The Isentropic Modified Chaplygin Gas Equations

This thesis studies the Cauchy problems with large initial data for the isentropic modified Chaplygin gas equations and isentropic Chaplygin gas magnetogasdynamics e-quations,respectively.By introducing the modified Chaplygin gas and Chaplygin gas pressure laws,with the help of phase plane analysis and Glimm's method,we establish the global existence of entropy solutions for the corresponding Cauchy problems.Chapter 2 briefly recalls some basic knowledge of nonlinear hyperbolic conservations and Glimm's method.In Chapter 3,we study the Cauchy problem for the isentropic modified Chaplygin gas equations.Based on analyzing the Riemann solutions to the isentropic modified Chap-lygin gas equations,by introducing the Riemann invariants,in the Riemann invariants plane we analyze the global behavior of the elementary waves and estimate the strength of these wave interactions.Then applying Glimm's difference scheme,we construct an approximate solution and prove its convergence for the Cauchy problem.Chapter 4 considers the Cauchy problem for the isentropic magnetogasdynamics e-quations with Chaplygin gas.By solving the Riemann problem of this system,with Glimm's method,we prove that the Cauchy problem exists a global entropy solution under certain reasonable hypotheses on the transverse magnetic field.