论文标题
具有陀螺效应的单基因喷雾模型的平均场极限推导
Mean-Field Limit Derivation of a Monokinetic Spray Model with Gyroscopic Effects
论文作者
论文摘要
在本文中，我们得出了一个具有陀螺效应的二维喷雾模型，它是模拟不可压缩流体与有限数量的固体颗粒之间相互作用的系统的平均场限制。该喷雾模型已由Moussa和Sueur（渐近肛门，2013年）研究，特别是在$ W^{1，\ infty} $互动的情况下建立了平均场极限。首先，我们证明了使用固定点方法的局部时间存在和模型的强溶液的独特性。然后，我们适应了Duerinckx和Cerfaty（DukeMath。J.，2020）的证明，以在库仑相互作用的情况下建立单基因制度中喷雾模型的平均场限制。
In this paper we derive a two dimensional spray model with gyroscopic effects as the mean-field limit of a system modeling the interaction between an incompressible fluid and a finite number of solid particles. This spray model has been studied by Moussa and Sueur (Asymptotic Anal., 2013), in particular the mean-field limit was established in the case of $W^{1,\infty}$ interactions. First we prove the local in time existence and uniqueness of strong solutions of a monokinetic version of the model with a fixed point method. Then we adapt the proof of Duerinckx and Serfaty (Duke Math. J., 2020) to establish the mean-field limit to the spray model in the monokinetic regime in the case of Coulomb interactions.
