Maria Colombo

EPFL, Lausanne

Nonuniqueness of solutions to the Euler equations with vorticity in a Lorentz space

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 that such uniqueness theorem fails in the class of vector fields \(u\) with uniformly bounded kinetic energy and vorticity in the Lorentz space \(L^{1, \infty}\) (joint work with Elia Brué).