Global Solutions Of The Two-dimensional Generalized Zakharov System With Magnetic Fields

Thesis is concerned with the Cauchy problem for the two-dimensional gen-eralized Zakharov system with magnetic fields,which is a basic model for describing plasma motion under the interaction of magnetic field and laser in quantum mechanics.It has important applications in industry,agriculture,medicine and so on.First,in the natural energy space H~1× H~1,we prove the local well-posedness of the system by using contraction mapping principle and Strichartz estimate,and give the conservation law of mass and the conservation law of energy for the two-dimensional generalized Zakharov system.Then,we give the sufficient conditions for the existence of global solutions of the system in the case of L~2-critical and subcritical,respectively.At the same time,we prove the existence of blow-up solutions for the system in the case of L~2-critical and supercritical,respectively.Finally,we discusse the dynamical properties of blow-up solutions for the two-dimensional generalized Zakharov system,and obtain the lower bound estimate for the blow-up rate of blow-up solutions.