Accepted Paper

Inserted: 21 aug 2021
Last Updated: 8 aug 2023

Journal: Communications in Mathematical Physics
Year: 2021

Abstract:

For the two dimensional Euler equations, a classical result by Yudovich states that solutions are unique in the class of bounded vorticity; it is a celebrated open problem whether this uniqueness result can be extended in other integrability spaces. We prove in this note that such uniqueness theorem fails in the class of vector fields $u$ with uniformly bounded kinetic energy and vorticity in the Lorentz space $L^{1, \infty}$.

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