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In this paper we study the initial value problem of the non-relativistic Vlasov-Darwin system with generalized variables (VDG). We first prove local existence and uniqueness of a nonnegative classical solution to VDG in three space variables, and establish the blow-up criterion. Then we show that it converges to the well-known Vlasov-Poisson system when the light velocity $c$ tends to infinity in a pointwise sense.
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참고문헌 (33)
참고문헌 신청
K. Asano / 1986 / On local solutions of the initial value problem for the Vlasov-Maxwell equation / Comm. Math. Phys. 106(4):551~568
C. Bardos / 1985 / Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data / Ann. Inst. H. Poincare Anal. Non Lineaire 2(2):101~118
J. Batt / 1977 / Global symmetric solutions of the initial value problem of stellar dynamics / J. Differential Equations 25(3):342~364
S. Bauer / 2005 / The Darwin approximation of the relativistic Vlasov-Maxwell system / Ann. Henri Poincare 6(2):283~308
S. Benachour / 2003 / Global existence for the Vlasov-Darwin system in ${\mathbb{R}}^3$ for small initial data / Math. Methods Appl. Sci. 26(4):297~319
C. Bardos / 1985 / Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data / Ann. Inst. H. Poincare Anal. Non Lineaire 2(2):101~118
J. Batt / 1977 / Global symmetric solutions of the initial value problem of stellar dynamics / J. Differential Equations 25(3):342~364
S. Bauer / 2005 / The Darwin approximation of the relativistic Vlasov-Maxwell system / Ann. Henri Poincare 6(2):283~308
S. Benachour / 2003 / Global existence for the Vlasov-Darwin system in
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