Control of velocities generated in a two—dimensional collisionless plasma with symmetry

Abstract

The Cauchy Problem for the relativistic Vlasov–Maxwell equations is studied in two dimensions. The Cauchy data E₀, B₀ of the fields, and the initial density f₀ of the plasma, are assumed to be smooth and to decay at infinity, and are to satisfy the usual constraints. When this data is restricted to be cylindrically symmetric, the v –support of the plasma density is shown to be bounded on every bounded time interval. However, a shock could still presumably be formed at very large times.