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

doi:10.1007/s10473-023-0507-7

Abstract

Abstract: We investigate the global classical solutions of the non-relativistic Vlasov-Darwin 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 $\frac{1}{c^2}$ as the speed of light $c$ tends to infinity for all time. Moreover, we obtain rigorously an asymptotic estimate of the difference between the two systems.

Key words: Vlasov-Darwin system, generalized variables, global classical solution, classical limit

CLC Number:

35Q83

Yaxian Ma, Xianwen Zhang. GLOBAL CLASSICAL SOLUTIONS AND THE CLASSICAL LIMIT OF THE NON-RELATIVISTIC VLASOV-DARWIN SYSTEM WITH SMALL INITIAL DATA^*[J].Acta mathematica scientia,Series B, 2023, 43(5): 2043-2060.

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

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