Initial Value Problems For Generalized Isentropic Magnetogasdynamics

The isentropic magnetogasdynamics can be used to govern the motion of isentropi-cally compressible fluids,subject to a transverse magnetic field.In this thesis,the initial problem for a kind of the generalized isentropic magnetogasdynamics is considered.Chapter 1,the study of the isentropic magnetogasdynamics and zero-pressure flow is introduced,and the work of this thesis is also stated.Chapter 2,Riemann solutions of the generalized zero-pressure flow are recalled.Chapter 3,Riemann problem and limiting behaviors of Riemann solutions for the generalized isentropic magnetogasdynamics are studied as the pressure and magnetic field vanish.First of all,under a general state equation of gas,using characteristic and phase plane analysis methods,the dependence of Riemann solutions to parameters for this sys-tem are discussed,five different configurations of Riemann solutions are obtained.Then it is shown that,when the pressure and magnetic field vanish,any Riemann solution containing two shock waves of the generalized isentropic magnetogasdynamics tends to a delta-shock solution to the generalized zero-pressure flow,and the intermediate density between the two shocks tends to the sum of a step function and a weighted ?-measure function;any Riemann solution containing two rarefaction waves of the generalized isen-tropic magnetogasdynamics tends to a two-contact-discontinuity solution to the general-ized zero-pressure flow,and the intermediate density between the two rarefaction waves tends to a vacuum state.Chapter 4,Cauchy problem for the generalized isentropic magnetogasdynamics is considered.Under certain assumptions,with the aid of the local existence and uniqueness of C1 solution of quasilinear hyperbolic equations,the global existence and uniqueness of continuous and piecewise C1 solution for this Cuachy problem is established by uniform a priori estimate.