零压等熵的磁场气体动力学系统的柯西问题

Cauchy Problem for Zero-pressure Isentropic Magnetogasdynamics Equations

零压等熵的磁场气体动力学方程组是等熵的磁场气体动力学系统在忽略压力效应后而得到的数学模型,本文主要研究零压等熵的磁场气体动力学方程组的一类初值问题,本文研究该系统的柯西问题,借助局部解的存在唯一性定理,通过一致先验估计,在适当的初值假设条件下,证明了该柯西问题整体C1解的存在唯一性,并给出古典解的生命期估计。

Zero-pressure isentropic magnetogasdyrtamics equations is a mathematical model obtained by neglecting pressure in the isentropic magnetogasdynamics systems, In this thesis Cauchy problem for the systems is studied. With the help of theorem of the local existence and uniqueness, by using uniform a priori estimates, under suitable condition of initial values, the global existence and uniqueness of Cl solutions is proved, and the life span of classical solutions is given.