Higher order regularity of nonlinear Fokker-Planck PDEs with respect to the measure component
نویسندگان
چکیده
In this article, we establish a general formula for higher order linear functional derivatives the composition of an arbitrary smooth on 1-Wasserstein space with solution Fokker-Planck PDE. This has important links theory propagation chaos and mean-field games. Dans cet nous établissons une formule générale pour les dérivées fonctionnelles linéaires d'ordre supérieur la d'une fonctionnelle régulière arbitraire sur l'espace avec EDP de Fokker-Planck. Cette des liens importants théorie du et jeux à champ moyen.
منابع مشابه
Regularity of Weak Solutions of the Nonlinear Fokker-planck Equation1
We study regularity properties of weak solutions of the degenerate parabolic equation ut + f(u)x = K(u)xx, where Q(u) := K ′(u) > 0 for all u 6= 0 and Q(0) = 0 (e.g., the porous media equation, K(u) = |u|m−1u, m > 1). We show that whenever the solution u is nonnegative, Q(u(·, t)) is uniformly Lipschitz continuous and K(u(·, t)) is C-smooth and note that these global regularity results are opti...
متن کاملOn the higher order corrections to the Fokker–Planck equation
The Rayleigh model of nonlinear Brownian motion is revisited in which the heavy particle of mass M interacts with ideal gas molecules of mass m5M via instantaneous collisions. Using the van Kampen method of expansion of the master equation, nonlinear corrections to the Fokker–Planck equation are obtained up to sixth order in the small parameter l 1⁄4 ffiffiffiffiffiffiffiffiffiffiffi m=M p ; im...
متن کاملGlobal L theory and regularity for the 3D nonlinear Wigner–Poisson–Fokker–Planck system
A global existence, uniqueness and regularity theorem is proved for the simplest Markovian Wigner–Poisson–Fokker–Planck model incorporating friction and dissipation mechanisms. The proof relies on Green function and energy estimates under mild formulation, making essential use of the Husimi function and the elliptic regularization of the Fokker– Planck operator. AMS Subject classification: 35Q4...
متن کاملGlobal regularity of solutions of coupled Navier-Stokes equations and nonlinear Fokker Planck equations
We provide a proof of global regularity of solutions of coupled Navier-Stokes equations and Fokker-Planck equations, in two spatial dimensions, in the absence of boundaries. The proof yields a priori estimates for the growth of spatial gradients. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 35Q30, 82C31, 76A05.
متن کاملNonlinear Fokker-Planck Navier-Stokes Systems
We consider Navier-Stokes equations coupled to nonlinear FokkerPlanck equations describing the probability distribution of particles interacting with fluids. We describe relations determining the coefficients of the stresses added in the fluid by the particles. These relations link the added stresses to the kinematic effect of the fluid’s velocity on particles and to the inter-particle interact...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2021
ISSN: ['0021-7824', '1776-3371']
DOI: https://doi.org/10.1016/j.matpur.2021.04.005