On the Cauchy problem for the magnetic Zakharov system

Abstract

In this paper, we study the Cauchy problem of the magnetic type Zakharov system which describes the pondermotive force and magnetic field generation effects resulting from the non-linear interaction between plasma-wave and particles. By using the energy method to derive a priori bounds and an approximation argument for the construction of solutions, we obtain local existence and uniqueness results for the magnetic Zakharov system in the case of $d=2,3$