Large, global solutions to the Navier-Stokes equations, slowly varying in one direction

By Jean-Yves Chemin, Isabelle Gallagher. 2007

98 citations recorded by the source corpus.

In to previous papers by the 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 aim of this article is to provide new examples of arbitrarily large initial data giving rise to global solutions, in the whole space. Contrary to the previous examples, the initial data has no particular oscillatory properties, but varies slowly in one direction. The proof uses the special structure of the nonlinear term of the equation.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ad7ebc86b56cb9039c7d4ddbe7482cd9d757a2c3

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Global regularity for some classes of large solutions to the Navier-Stokes equations (2008, background): “Similarly in [6], that fact was used to prove a global existence result for large data which are slowly varying in one direction.”