On plane oscillations of the cold plasma in a constant magnetic field

TL;DR

This paper investigates the conditions for the global existence or finite-time blowup of classical solutions in 2D cold plasma models with constant magnetic and electric fields, focusing on symmetric solutions.

Contribution

It provides new insights into the initial data conditions that ensure solution longevity or finite-time blowup in cold plasma equations with magnetic and electric fields.

Findings

Conditions for global existence of solutions.

Criteria for finite-time blowup.

Special analysis of axially symmetric solutions.

Abstract

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 blowup. Particular attention is paid to the class of solutions with axial symmetry.