Uniqueness for 2D Euler and transport equations via extrapolation

2023/06/13 by Dominguez, Oscar, Milman, Mario
#46M35 #76B03 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2306.08082

Abstract

Using extrapolation theory, we develop a new framework to prove the uniqueness of solutions for transport equations. We apply our methodology to unify and extend the classical results of Yudovich and Vishik for 2D Euler equations. In particular, we establish the uniqueness for the Euler flow whose vorticity belongs to new scales of function spaces that contain both Yudovich spaces and BMO. We give a self contained presentation.

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• Unbounded Yudovich Solutions of the Euler Equations
• Non-uniqueness and energy dissipation for 2D Euler equations with vorticity in Hardy spaces