The Vlasov-Maxwell-Landau System Near Maxwellians With Strong Background Magnetic Field

Usually,the motion of a fully ionized plasma of electrons and ions is generally governed by the Vlasov-Maxwell-Landau system.In this paper,we are concerned with the construction of global-in-time solutions of the Cauchy problem of the Vlasov-Maxwell-Landau system near Maxwellians in the presence of a strong magnetic field,where the given background mag-netic field can be any given non-zero constant.The key point of this paper is to deduce the dissipation estimates of the electronic field and strong background magnetic field.First,we can derive the dissipation estimates of the main part Pf(t,x,v)of function f(t,x,v)and the electromagnetic field[E(t,x),B(t,x)],then we can derive the prior estimates of solution(?),finally,we can deduce the main theorem of this paper.