Uniqueness for 2D Euler and transport equations via extrapolation
Analysis of PDEs
2024-12-31 v2 Functional Analysis
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.
Cite
@article{arxiv.2306.08082,
title = {Uniqueness for 2D Euler and transport equations via extrapolation},
author = {Oscar Dominguez and Mario Milman},
journal= {arXiv preprint arXiv:2306.08082},
year = {2024}
}
Comments
We provide a new proof of Theorem 1.1 and show that our method gives uniqueness for a large class of active scalar equations