A lower bound on blowup rates for the 3D incompressible Euler equation   and a single exponential Beale-Kato-Majda type estimate
  We prove a Beale-Kato-Majda type criterion for the loss of regularity for solutions of the incompressible Euler equations in $H^{s}({\mathbb R}^3)$, for $s>\frac52$. Instead of double exponential estimates of Beale-Kato-Majda type, we obtain a single exponential bound on $\|u(t)\|_{H^s}$ involving the length parameter introduced by P. Constantin in \cite{co1}. In particular, we derive lower bounds on the blowup rate of such solutions. 
Thomas Chen, Nata\v{s}a Pavlovi\'c
math.AP math-ph math.MP