一类带非牛顿位势的广义Vlasov方程

A class of generalized Vlasov equations with non-Newtonian potential

研究了一类带非牛顿位势的广义Vlasov方程,该方程描绘了在非牛顿位势作用下粒子的运动情形。基于压缩映像原理,在没有截断速度的情况下,利用抛物方程解的正则性证明了在p≥2时mild解的整体存在唯一性,以及1<p<2时mild解的局部存在唯一性。该结论推广了文献[7]在截断速度条件下的部分结论。

This paper is concerned with a class of generalized Vlasov equations which models the transports of particles under the influence of the non-Newtonian potential.Without requiring the hypothesis of cut-off velocity,the existence and uniqueness of global mild solution with p≥2 and local mild solution with 1〈p〈2 are established by the contraction mapping principle in one di-mension.The proof is based on Green function techniques and parabolic regularization.This result generalizes the previous result by Yan[7],which deals with the solution with cut-off velocity.