一类带非牛顿位势的广义Vlasov方程
首发时间:2015-12-22
摘要: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 时mild解的整体存在唯一性,以及 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。
关键词: 广义Vlasov方程; 抛物正则性; 非牛顿位势; Mild解; 压缩映像原理
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A class of generalized Vlasov equations with non-Newtonian potential
Abstract: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 and local mild solution with are established by the contraction mapping principle in one dimension. 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.
Keywords: generalized Vlasov equation parabolic regularization non-Newtonian potential mild solution contraction mapping principle
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