论文标题
一类奇异弗拉索夫方程的本地适应性
Local well-posedness for a class of singular Vlasov equations
论文作者
论文摘要
在本文中，我们研究了一个奇异的弗拉索夫系统，其中力场具有（分数）衍生物$ d^α$的平滑度，其中$α> 0 $。我们在Sobolev空间中证明了局部良好的性能，而无需限制数据。这与$α= 0 $的情况形成鲜明对比，后者在Sobolev空间中以供一般数据进行了鲜明的对比。
In this article we study a singular Vlasov system on the torus where the force field has the smoothness of a (fractional) derivative $D^α$ of the density, where $α>0$. We prove local well-posedness in Sobolev spaces without restriction on the data. This is in sharp contrast with the case $α=0$ which is ill-posed in Sobolev spaces for general data.
