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arXiv · 2108.09469

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

Elia Brué·Maria Colombo
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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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Elia Brué, Maria Colombo. 2021-08-21. Nonuniqueness of solutions to the Euler equations with vorticity in a Lorentz space. https://arxiv.org/abs/2108.09469

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