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

2024/10/31 by Leonardo Roveri, Roveri, Leonardo, Francesco Triggiano +1 · 1 citation
Earth and Planetary Sciences · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2410.24040

openalex publication_date 2024/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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