Forthcoming Seminars › Seminar Series

OxPDE Lunchtime Seminar

Thu, 05/05/2011
12:30 		Jose Rodrigo (University of Warwick) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
On the evolution of almost-sharp fronts for the surface quasi-geostrophic equation
I will describe recent work with Charles Fefferman on a construction of families of analytic almost-sharp fronts for SQG. These are special solutions of SQG which have a very sharp transition in a very thin layer. One of the main difficulties of the construction is the fact that there is no formal limit for the family of equations. I will show how to overcome this difficulty, linking the result to joint work with C. Fefferman and Kevin Luli on the existence of a "spine" for almost-sharp fronts. This is a curve, defined for every time slice by a measure-theoretic construction, that describes the evolution of the almost-sharp front.
Thu, 19/05/2011
12:30 		Dominic Breit (University of Saarbrucken) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
On stationary motions of Prandtl-Eyring fluids in 2D
We prove the existence of weak solutions to steady Navier Stokes equations
$$\text{div}\, \sigma+f=\nabla\pi+(\nabla u)u.$$
Here $ u:\mathbb{R}^2\supset \Omega\rightarrow \mathbb{R}^2 $ denotes the velocity field satisfying $ \text{div}\, u=0 $, $ f:\Omega\rightarrow\mathbb{R}^2 $ and $ \pi:\Omega\rightarrow\mathbb{R} $ are external volume force and pressure, respectively. In order to model the behavior of Prandtl-Eyring fluids we assume
$$\sigma= DW(\varepsilon (u)),\quad W(\varepsilon)=|\varepsilon|\log (1+|\varepsilon|).$$
A crucial tool in our approach is a modified Lipschitz truncation preserving the divergence of a given function.
Thu, 26/05/2011
12:30 		Fabrice Planchon (Universite de Nice (France)) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
Going beyond Serrin's endpoint regularity criterion for Navier-Stokes
Solutions which are time-bounded in L^3 up to time T can be continued past this time, by a landmark result of Escauriaza-Seregin-Sverak, extending Serrin's criterion. On the other hand, the local Cauchy theory holds up to solutions in BMO^-1; we aim at describing how one can obtain intermediate regularity results, assuming a priori bounds in negative regularity Besov spaces. This is joint work with J.-Y. Chemin, Isabelle Gallagher and Gabriel Koch.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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