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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 |
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Vol. 1 (2019), No. 2, 273–293
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Abstract |
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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. |
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Keywords
Navier–Stokes equations, blow-up
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Mathematical Subject Classification 2010
Primary: 76D05
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Milestones
Received: 22 January 2018
Accepted: 10 February 2018
Published: 14 May 2018
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Authors |
| Jean-Yves Chemin | |
| Laboratoire J.-L. Lions, UMR
7598 Université Pierre et Marie Curie Sorbonne Université 75230 Paris Cedex 05 France |
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| Isabelle Gallagher | |
| Ecole Normale Supérieure 75005 Paris France |
Université Paris-Diderot Sorbonne Paris-Cité 75013 Paris France |
