Global regularity for some classes of large solutions to the Navier-Stokes equations

Abstract

In previous works by the first two authors, classes of initial data to the three-dimensional, incompressible Navier-Stokes equations were presented, generating a global smooth solution although the norm of the initial data may be chosen arbitrarily large. The main feature of the initial data considered in one of those studies is that it varies slowly in one direction, though in some sense it is “well-prepared” (its norm is large but does not depend on the slow parameter). The aim of this article is to generalize that setting to an “ill prepared” situation (the norm blows up as the small parameter goes to zero). As in those works, the proof uses the special structure of the nonlinear term of the equation.

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Authors

Jean-Yves Chemin

Université Pierre et Marie Curie
Paris
France

Isabelle Gallagher

Université Paris Diderot
Paris
France

Marius Paicu

Université Paris Sud
Orsay
France