An improved bound on the support diameter of nonnegative planar Euler vorticity

Abstract

We prove an $O(t^{1/4})$ bound on the support radius of nonnegative planar Euler vorticity with compactly supported $L^1$ initial data, removing the logarithmic factors from the classical confinement estimates. The result holds in the symmetrized vorticity formulation. A factorization of the interaction kernel yields a quadratic convolution inequality for high-order moments. Retaining this convolution allows an elementary comparison for finite sums of moments to control the full support. We also prove that the squared support radius is Hölder continuous in time with exponent $1/2$.