= Planar vorticity velocity kernel
{title2=$K(z)=\pm z^\perp/(2\pi|z|^2)$}
= Planar Biot-Savart kernel
{synonym}
The <velocity> induced by planar <vorticity> is a <convolution> with this kernel, whose sign depends on the <stream function> and vorticity conventions. Its magnitude is $(2\pi|z|)^{-1}$ and its derivative is bounded by $C|z|^{-2}$. Splitting the convolution at radius $R$ gives $\|K*\omega\|_\infty\leq R\|\omega\|_\infty+\|\omega\|_1/(2\pi R)$. The same singularity yields a <log-Lipschitz modulus>, enough for a <Yudovich characteristic flow>.
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