## Global solutions for the Navier-Stokes equations with some large initial data

Series
PDE Seminar
Time
Tuesday, March 2, 2010 - 3:05pm for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Marius Paicu – Université Paris-Sud
Organizer
Zhiwu Lin
We consider the three dimensional Navier-Stokes equations with a large initial data and we prove the existence of a global smooth solution. The main feature of the initial data is that it varies slowly in the vertical direction and has a norm which blows up as the small parameter goes to zero. Using the language of geometrical optics, this type of initial data can be seen as the ill prepared" case. Using analytical-type estimates and the special structure of the nonlinear term of the equation we obtain the existence of a global smooth solution generated by this large initial data. This talk is based on a work in collaboration with J.-Y. Chemin and I. Gallagher and on a joint work with Z. Zhang.