# CAMP/Nonlinear PDEs Seminar

The seminar meets regularly on wednesday at 4pm in Eckhart 202. We also have special seminars during other days.

### Spring 2012 Schedule.

March 28th
Jun Cheng Wei, Chinese University of Hong Kong. Eckhart 202. 4pm.
On $SU(N+1)$ Toda system: Classification and Applications
Abstract: We classify all solutions to the $SU(N+1)$ Toda system. As a consequence, we construct non-topological solutions to $SU(3)$ and $B_2$ Chern-Simons system.
April 11th
Pablo Pedregal, Universidad de Castilla-La Mancha. Eckhart 202. 4pm.
A variational proposal for Navier-Stokes.
A variational approach, consisting in minimizing a certain error functional, will be set up to study the Navier-Stokes system. The functional-analytical scenario is chosen so that feasible vector fields, if they turn out to be weak solutions in a suitable sense, are automatically smooth. The error functional measures how far" feasible fields are from being a solution. Once the basic ingredients are described, the task is two-fold: 1. Prove existence of minimizers for the error. 2. Show that the minimum value vanishes. Non-standard tools are required to cover these two steps. On the one hand, coercivity fails both in dimension 2 and 3. For dimension 2, a substitute can be found taking advantage of the natural scaling. In dimension 3, this is not possible due to supercriticality. The job of showing that the minimum vanishes requires to look at optimality conditions and the linearized system.
April 18th
Ovidiu Munteanu, Columbia University. Eckhart 202. 4pm.
This is a survey of some recent development in the study of Ricci solitons. These manifolds are very important in the study of singularities of the Ricci flow and are natural extensions of Einstein manifolds. Among other things, we will discuss curvature estimates, volume growth and topology at infinity. Understanding certain partial differential equations on Ricci solitons is very important for this study.
May 2nd
Regis Monneau, University Paris - Est. Eckhart 202. 4pm.
Hamilton-Jacobi equations on a jonction and application to traffic flow.
This work is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a junction'', that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison principle. We also prove existence and stability of solutions. The two challenging difficulties are the singular geometry of the domain and the discontinuity of the Hamiltonian. As far as discontinuous Hamiltonians are concerned, these results seem to be new. They are applied to the study of some models arising in traffic flows. The techniques developed in the present work provide new powerful tools for the analysis of such problems.
May 7th, 8th and 9th
These are the Zygmund-Calderón Lectures:
Demetrios Christodoulou, ETH. Zygmund-Calderón Lectures in Analysis.
May 7th to May 18th
Concentration period on nonlinear elliptic PDEs.
There will be special activities during these two weeks.
May 11th ( Friday )
Alexander Kiselev, UW Madison. Eckhart 202. 4pm.
TBA
TBA
May 16th
Xavier Cabre, UPC Barcelona. Eckhart 202. 4pm.
Antisymmetry and isoperimetry for some elliptic problems with weights.
May 23rd
Lisa Fauci, Tulane University. Eckhart 202. 4pm.
Calcium-driven dynamics of undulatory swimmers: a tale of two Reynolds numbers.
Locomotion due to body undulations is observed across the entire spectrum of swimming organisms, from microorganisms to fish. The internal force generating mechanisms range from the action of dynein molecular motors within a mammalian sperm to muscle activation in lamprey. We will present recent progress in building multiscale computational models that couple biochemistry, passive elastic properties and active force generation with a surrounding fluid for these two swimmers.
May 29th, 30th and 31st
Jeff Rauch, University of Michigan. Amick lectures.
These are the special Amick lecture series.

You can also check the calendar of visitors.
For questions, contact Luis Silvestre at

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