Abstract
AbstractFor 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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1
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∞
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Funder
Università Commerciale Luigi Bocconi
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
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