Communications in Mathematical Physics

, Volume 314, Issue 1, pp 265–280

A Lower Bound on Blowup Rates for the 3D Incompressible Euler Equation and a Single Exponential Beale-Kato-Majda Type Estimate


DOI: 10.1007/s00220-012-1523-y

Cite this article as:
Chen, T. & Pavlović, N. Commun. Math. Phys. (2012) 314: 265. doi:10.1007/s00220-012-1523-y


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 \({s>\frac{5}{2}}\) . 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 Constantin in (SIAM Rev. 36(1):73–98, 1994). In particular, we derive lower bounds on the blowup rate of such solutions.

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© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA