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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