# Analysis Seminar

#### Transport of BMO-Type Spaces by a Measure-Preserving Map and Applications to 2D Euler Equation

Speaker: Frederic Bernicot, University of Nantes

Location: Warren Weaver Hall 1314

Date: Tuesday, December 4, 2012, 10 a.m.

Synopsis:

We will present some sharp estimates about the transport of BMO-type spaces, via a bi-Lipschitz measure preserving map in the Euclidean space. More precisely, we are interested in inequalities of the following type: $$\| f(\phi) \|_X \lesssim C(\phi) \|f\|_X$$ where $$X$$ is a space like BMO, Lipschitz space, Hardy space, Carleson measure spaces .... and $$\phi$$ is a bi-Lipschitz measure preserving map. The aim is to prove such inequalities with a sharp constant $$C(\phi)$$. We want to emphasize how the "measure preserving" property allows us to get some improved inequalities. Then, we will explain how we can use this argument to describe a new framework for 2D Euler equations. We can define a space strictly containing $$L^\infty$$ where global well-posedness results can be proved with the vorticity living in this new space.