论文标题
Dean-Kawasaki方程式具有单数相互作用，并应用于动力学-KAC模型
Dean-Kawasaki Equation with Singular Interactions and Applications to Dynamical Ising-Kac Model
论文作者
论文摘要
受[Fehrman，Gess的启发；发明。 Math。，2023]和[Fehrman，Gess;拱。配给。机械。肛门，2024年]，我们考虑具有单数相互作用和相关噪声的Dean-Kawasaki方程，可以看作是波动的平均场限制。通过将ladyzhenskaya-serrodi-serrin条件施加在相互作用的内核上，建立了概率弱重新归一化的动力学溶液的存在。此外，在相互作用内核的差异的额外积分假设下，动力学公式方法被应用于导出路径唯一性，从而导致方程的强大范围。作为一种应用，我们获得了保守的随机部分微分方程的良好性，称为波动的ising-kac-kawasaki动力学，该方程铺平了关于川崎动态非线性波动的猜想，这是[giacomin，lebowitz，presutti提出的；数学。调查Monogr。，1999]。
Inspired by [Fehrman, Gess; Invent. Math., 2023] and [Fehrman, Gess; Arch. Ration. Mech. Anal., 2024], we consider the Dean-Kawasaki equation with singular interactions and correlated noise which can be viewed as fluctuating mean-field limits. By imposing the Ladyzhenskaya-Prodi-Serrin condition on the interaction kernel, the existence of probabilistic weak renormalized kinetic solutions is established. Further, under an additional integrability assumption on the divergence of the interaction kernel, a kinetic formulation approach is applied to derive pathwise uniqueness, leading to the strong well-posedness of the equation. As an application, we obtain the well-posedness of a conservative stochastic partial differential equations known as fluctuating Ising-Kac-Kawasaki dynamics, which paves a step on the conjecture concerning nonlinear fluctuations of Kawasaki dynamics proposed by [Giacomin, Lebowitz, Presutti; Math. Surveys Monogr., 1999].
