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Optimal Regularity for the 2D Euler Equations in the Yudovich class (2403.13691v1)
Published 20 Mar 2024 in math.AP
Abstract: We analyze the optimal regularity that is exactly propagated by a transport equation driven by a velocity field with BMO gradient. As an application, we study the 2D Euler equations in case the initial vorticity is bounded. The sharpness of our result for the Euler equations follows from a variation of Bahouri and Chemin's vortex patch example.
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