Vanishing Flux-perturbation Limits Of Solutions To The Isentropic Magnetogasdvnamics

The isentropic magnetogasdynamics can be used to describe the motion of an invis-cid and perfectly conducting compressible fluid, subject to a transverse magnetic field. This thesis is concerned with the limit behaviors of Riemann solutions to the isentropic magnetogasdynamics under flux perturbation. By introducing the polytropic gas and gen-eralized Chaplygin gas, with the help of characteristic and phase plane analysis methods, the Riemann problems of the corresponding perturbed systems are constructively solved. Furthermore, the limits of Riemann solutions are analyzed as the pressure, magnetic field and flux perturbation vanish. The thesis consists of two parts.The first part considers the isentropic magnetogasdynamics for polytropic gas. First-ly, the Riemann problem of the isentropic magnetogasdynamics under flux perturbation are solved, and five different configurations of Riemann solutions are constructed. Sec-ondly, we rigorously proved that, as the pressure, magnetic field and flux perturbation vanish, any Riemann solution containing two shock waves tends to a delta-shock solution to the zero-pressure flow; any Riemann solution containing two rarefaction waves tends to a vacuum solution to the zero-pressure flow, and the nonvacuum intermediate state in between tends to a vacuum state. Finally, we simulate the above limiting processes.The second part studies the isentropic magnetogasdynamics for generalized Chaply-gin gas. Based on solving the Riemann problem of this system with a flux perturbation, we rigorously analyze that, as the generalized Chaplygin gas pressure, magnetic field and flux perturbation vanish, any Riemann solution containing two shock waves tends to a delta-shock solution to the zero-pressure flow; any Riemann solution containing two rar-efaction waves tends to a vacuum solution to the zero-pressure flow. The numerical results are coincident with the theoretical analysis.