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Stochastic Lagrangian Flows for SDEs with rough coefficients

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arxiv 1911.05562 v4 pith:2CRWIW2B submitted 2019-11-13 math.PR math.AP

Guohuan Zhao This is my paper · ORCID
classification math.PRmath.AP
keywords stochasticflowscoefficientslagrangianroughsdesalmostapplication
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We prove the existence and uniqueness of Stochastic Lagrangian Flows and almost everywhere Stochastic Flows for non-degenearted SDEs with rough coefficients. As an application of our main result, we show that there exists a unique Stochastic Flow corresponding to each Leray-Hopf solution of 3D Navier-Stokes equation in the DiPerna-Lions sense.

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  1. Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations

    math.AP 2025-04 conditional novelty 7.0 of 10

    Weak solutions of the Euler and Navier-Stokes equations exist for which two different particle trajectories start from the same point, in sharp regularity ranges, both with and without Brownian noise.

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