On Plane Oscillations of the Cold Plasma in a Constant Magnetic Field

We consider a class of two-dimensional solutions of the cold plasma equations compatible with a constant magnetic field and a constant electric field. For this class, under various assumptions about the electric field, we study the conditions on the initial data that guarantee the global existence of the classical solution of the Cauchy problem for a given period of time or a finite time blow-up. Particular attention is paid to the class of solutions with axial symmetry.