Diagrams and Expansions of solutions of the 3-dim Navier-Stokes System

Yakov Sinai

Professor of Mathematics,
Princeton University

Date: Wednesday, March 05, 2008
Location: PSA 304
Time: 1:20-2:30pm

I shall consider the Fourier transform of the 3-dim Navier-Stokes system. There are some natural functional spaces in which local existence theorems are valid. In the limiting case of the so-called critical case the global existence theorem is valid for small initial condition while the situation with large initiual condition is completely open. In general, solutions can be represented as series of diagrams. Some estimates of these diagrams will be presented. The whole theory requires new notions of convolutions.