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Well-posedness of rough 2D Euler equation with bounded vorticity

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arxiv 2410.24040 v1 pith:776Z3GDP submitted 2024-10-31 math.AP

Leonardo Roveri , Francesco Triggiano This is my paper · ORCID
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keywords roughvorticityboundedequationeulerinitialsolutionadvected
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We consider the 2D Euler equation with bounded initial vorticity and perturbed by rough transport noise. We show that there exists a unique solution, which coincides with the starting condition advected by the Lagrangian flow. Moreover, the stability of the solution map with respect to the initial vorticity and the rough perturbation yields a Wong-Zakai result for fractional Brownian driving paths.

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  1. On the well-posedness of (nonlinear) rough continuity equations

    math.AP 2025-02 accept novelty 8.0 of 10

    Rough continuity and transport equations are well-posed for Osgood and DiPerna-Lions drifts, yielding a rough Yudovich theorem for 2D Euler and a continuous random dynamical system.

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