On the global wellposedness of the 3-D Navier-Stokes equations with large initial data

Details On the global wellposedness of the 3-D Navier-Stokes equations with large initial data On the global wellposedness of the 3-D Navier-Stokes equations with large initial data

2005-08-19

arxiv.org/abs/math/0508374v1

Mathematics

Analysis of PDEs

Scientific paper

We give a condition for the periodic, three dimensional, incompressible Navier-Stokes equations to be globally wellposed. This condition is not a smallness condition on the initial data, as the data is allowed to be arbitrarily large in the scale invariant space $ B^{-1}\_{\infty,\infty}$, which contains all the known spaces in which there is a global solution for small data. The smallness condition is rather a nonlinear type condition on the initial data; an explicit example of such initial data is constructed, which is arbitrarily large and yet gives rise to a global, smooth solution.

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