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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…