Asymptotic growth bounds for the Vlasov-Poisson system in convex bounded domains

Abstract

We consider smooth compactly supported solutions to the classical three-dimensional Vlasov-Poisson system in convex bounded domains. In the plasma physics case, we show that the size of the velocity support of the distribution function grows at most t 16 21 + for any > 0.

Asymptotic growth bounds for the Vlasov-Poisson system in a half space

“…In [6] it has been proved that the solutions of the Vlasov-Poisson system (1.1)-(1.3) in a domain Ω, with specular reflection boundary conditions and nonhomogeneous Neumann boundary conditions are globally defined in arbitrary convex domains Ω. [1] improved Hwang's estimates for the growth of the solutions. In a half space the global existence result was shown in [3] if the initial data f 0 is assumed to be constant in a neighbourhood of the singular set.…”