Abstract
Abstract
We consider the Vlasov–Poisson system with external magnetic field in a half-space with the Neumann boundary condition for the electric potential and specular reflection on a boundary. For arbitrary compactly supported initial density distribution functions, we obtain sufficient conditions for external magnetic field, which provide global existence of density distribution functions with compact supports lying at some distance from a boundary.
Reference21 articles.
1. A. A. Vlasov, ‘‘Vibrational properties of the electronic gas,’’ Zh. Eksp. Teoret. Fiz. 8, 291–318 (1938).
2. K. Miyamoto, Fundamentals of Plasma Physics and Controlled Fusion (Iwanami Book Service Centre, Tokyo, 1997).
3. J. Batt, ‘‘Global symmetric solutions of the initial value problem of stellar dynamics,’’ J. Differ. Equat. 25, 342–364 (1977).
4. K. Pfaffelmoser, ‘‘Global classical solutions of the Vlasov–Poisson system in three dimensions for general initial data,’’ J. Differ. Equat. 95, 281–303 (1992).
5. J. Schäffer, ‘‘Global existence of smooth solutions to the Vlasov–Poisson system in three dimensions,’’ Comm. Part. Diff. Equat. 16, 1313–1335 (1991).