Vol. 1, No. 2, 2019

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A nonlinear estimate of the life span of solutions of the three dimensional Navier–Stokes equations

Jean-Yves Chemin and Isabelle Gallagher

Vol. 1 (2019), No. 2, 273–293

The purpose of this article is to establish bounds from below for the life span of regular solutions to the incompressible Navier–Stokes system, which involve norms not only of the initial data, but also of nonlinear functions of the initial data. We provide examples showing that those bounds are significant improvements to the one provided by the classical fixed point argument. One of the important ingredients is the use of a scale-invariant energy estimate.

Navier–Stokes equations, blow-up
Mathematical Subject Classification 2010
Primary: 76D05
Received: 22 January 2018
Accepted: 10 February 2018
Published: 14 May 2018
Jean-Yves Chemin
Laboratoire J.-L. Lions, UMR 7598
Université Pierre et Marie Curie
Sorbonne Université
75230 Paris Cedex 05
Isabelle Gallagher
Ecole Normale Supérieure
75005 Paris
Université Paris-Diderot
Sorbonne Paris-Cité
75013 Paris