On scale-invariant solutions to the Navier Stokes equation

Special Colloquium

Wednesday, January 23, 2013 : 3:30pm to 4:30pm

University Park Campus
Kaprelian Hall
414


Hao Jia, University of Minnesota

Abstract: The Navier Stokes equation has a natural scaling invariance. In this talk we will discuss a result that for every scale-invariant initial data there is a global scale invariant solution (smooth for positive times) to the Navier Stokes equation. It appears that the result is not accessible by the usual perturbation methods. The proof uses a topological tool (degree theory), and seems to suggest non-uniqueness. We will also present some new estimates which seem to be of independent interest. Joint work with V. Sverak