Cauchy problem for an isentropic magnetogasdynamic system

This paper investigates the Cauchy problem for an isentropic magnetogasdynamic system. Under certain reasonable hypotheses on the initial data, we obtain the global existence and uniqueness of the C1C1 solution to the system. Meanwhile, when the hypotheses on the initial data do not hold, we obtain the blow-up phenomena of the C1C1 solution to the system. The bounds of the solution are shown to depend on the parameter ν  , which characterizes a one-dimensional plane flow (ν=0ν=0) or a three-dimensional cylindrically symmetric flow (ν=1ν=1); it is shown that the existence of the finite time singularity is significantly influenced by the magnetic field strength present in the flow along with the initial data.