Distribution Dependent SDEs for Navier-Stokes Type Equations

TL;DR

This paper introduces a new class of distribution-dependent stochastic differential equations designed to model Navier-Stokes type equations with singular second order operators, establishing their well-posedness and regularity.

Contribution

It proposes a novel framework of distribution-dependent SDEs tailored for Navier-Stokes equations with singular operators, including well-posedness and regularity results.

Findings

Well-posedness of the proposed SDEs

Regularity estimates for solutions

Framework applicable to Navier-Stokes type equations

Abstract

To characterize Navier-Stokes type equations where the Laplacian is extended to a singular second order differential operator, we propose a class of SDEs depending on the distribution in future. The well-posedness and regularity estimates are derived for these SDEs.