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math.AP2026
An improved bound on the support diameter of nonnegative planar Euler vorticity
Daomin Cao, Junhong Fan, Guodong Wang
We prove an bound on the support radius of nonnegative planar Euler vorticity with compactly supported initial data, removing the logarithmic factors from the cl…
math.AP2026
Gradient growth and relaxation to jump profiles for 3-fold symmetric scale-invariant Euler flows
Daomin Cao, Junhong Fan, Guolin Qin
We consider long-time behavior of the zero-homogeneous solutions with 3-fold symmetry to the two-dimensional Euler equation. This is the remaining case in the relaxation theory of…
math.AP2026
Growth of vorticity gradient for the Euler equation on the sphere
Daomin Cao, Junhong Fan, Guolin Qin
We prove that for solutions of the Euler equation on the sphere, the vorticity gradient can grow at most double-exponentially in time, and we show that this upper bound is sharp by…