论文标题
McKean-Vlasov SDE和SPDE具有局部单调系数
McKean-Vlasov SDE and SPDE with Locally Monotone Coefficients
论文作者
论文摘要
在本文中，我们主要研究了一类McKean-Vlasov随机（部分）微分方程的强大和弱的良好性。主要的存在和唯一性结果表明，我们只需要对系数上的某些局部假设，即状态变量和分布变量中的局部单调条件，这会导致一些必不可少的难度，因为McKean-Vlasov Stochastic方程的系数通常非局限性。此外，在这些弱假设下，McKean-Vlasov随机方程也得出了较大的偏差原理。主要结果的广泛应用由各种具体示例，例如颗粒状介质方程，等离子体类型模型，动力学方程，McKean-Vlasov类型多孔介质方程和Navier-Stokes方程。特别是，我们可以删除或放松以前对这些模型施加的一些典型假设。
In this paper we mainly investigate the strong and weak well-posedness of a class of McKean-Vlasov stochastic (partial) differential equations. The main existence and uniqueness results state that we only need to impose some local assumptions on the coefficients, i.e. locally monotone condition both in state variable and distribution variable, which cause some essential difficulty since the coefficients of McKean-Vlasov stochastic equations typically are nonlocal. Furthermore, the large deviation principle is also derived for the McKean-Vlasov stochastic equations under those weak assumptions. The wide applications of main results are illustrated by various concrete examples such as the granular media equations, plasma type models, kinetic equations, McKean-Vlasov type porous media equations and Navier-Stokes equations. In particular, we could remove or relax some typical assumptions previously imposed on those models.
