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Compactly Supported Strong Ill-Posedness of the Two-Dimensional Euler Flow in $W^{3,1}(\mathbb R^2)$
We prove strong ill-posedness for the two-dimensional incompressible Euler equation in the endpoint velocity space $W^{3,1}_σ(\mathbb R^2)$. Given any compactly supported smooth divergence-free background and any $δ>0$, we construct a single compactly supported divergence-free datum within $δ$ of th
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