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

2011/07/31 by Thomas Chen, Nataša Pavlović · 6 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Compressibility #Euler's formula #Exponential function #Exponential type #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Type (biology) #Upper and lower bounds #math-ph #math.AP #math.MP #msc:76B03

paper · pdf · doi:10.1007/s00220-012-1523-y

published in Communications in Mathematical Physics 314(1), 265-280 (Springer Science+Business Media) · AMS Latex, 15 pages

openalex publication_date 2012/07/17 · openalex created_date 2016/06/24 · arxiv created 2016/08/13 · arxiv updated 2017/08/23 · openalex updated_date 2026/08/05

Abstract

We prove a Beale-Kato-Majda type criterion for the loss of regularity for solutions of the incompressible Euler equations in H^s(\mathbb R³), 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 \citeco1. In particular, we derive lower bounds on the blowup rate of such solutions.

Citations

• Geometric constraints on potentially