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

Abstract

In [7] the Vlasov-Poisson system was investigated in a half space and then global existence result was obtained. In this paper, we show that the size of the velocity support of the distribution function grows at most like the power 16 21 of the time variable.

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

“…A new proof of global modifying Pfaffelmoser's idea [16] was recently proved in [13]. [1] improved Hwang's estimates for the growth of the solutions. For general convex bounded domains but with the Nenmann boundary condition for φ, the global well-posedness was shown in [11].…”

“…For classical Vlasov-Poisson system if the Ω = R 3 , different upper bounds of Q(t) were established by many authors see, e.g. : [15,17,4], and if Ω = R 3 + , recently sub-linear estimate was obtained in [1]. For the system (1.1)-(1.5), so far only the following upper bound was obtained :for any > 0…”