GLOBAL CLASSICAL SOLUTIONS AND THE CLASSICAL LIMIT OF THE NON-RELATIVISTIC VLASOV-DARWIN SYSTEM WITH SMALL INITIAL DATA

We investigate the global classical solutions of the non-relativistic Vlasov-D arwin system with generalized variables(VDG) in three dimensions.We first prove the global existence and uniqueness for small initial data and derive the decay estimates of the Darwin potentials.Then,we show in this framework that the solutions converge in a pointwise sense to solutions of the classical Vlasov-Poisson system(VP) at the asymptotic rate of 1/c² as the speed of light c tends to infinity for al...     

ASYMPTOTIC GROWTH BOUNDS FOR THE VLASOV-POISSON SYSTEM WITH RADIATION DAMPING

We consider asymptotic behaviors of the Vlasov-Poisson system with radiation damping in three space dimensions.For any smooth solution with compact support,we prove a sub-linear growth estimate of its velocity support.As a consequence,we derive some new estimates of the charge densities and the electrostatic field in this situation.