Lipschitz Lectures

Studies in dynamics, coherent structures and stability

Robert L. Pego, Carnegie Mellon University

 

Date: June 20 - 29, 2017
Time: Tuesday 2 - 4 p.m., Wednesday 12 - 2 p.m., Thursday 2 - 4 p.m.
Location: Mathematik-Zentrum, Lipschitz Lecture Hall, Endenicher Allee 60, Bonn

 


Abstract:

The plan is to tell the stories of three examples:

(i) Instability of least action for free fluids.

Two famous least-action principles for fluids lead to
Arnold's geodesic interpretation of incompressible fluid flow,
and the Monge-Kantorivich optimal transportation problem.
We show that these principles are directly related to each other
through an instability in an optimal shape deformation problem.

(ii) Stability in models of solitary water waves.

In many cases, the stability of solitary waves can be
established by study of constrained minimization of energy-momentum functionals.
The classic water wave of Scott Russell is not one of those cases, however.
We will describe how nonlinear stability can be established for
a model water-wave equation with indefinite variational structure,
through judicious use of the Boussinesq-KdV approximation and
virial energy-propagation estimates.

(iii) Coagulation-fragmentation model of animal group size.

A remarkable data analysis and modeling study of ocean fisheries
by H.-S. Niwa motivates the study of certain kinetic equations
for cluster-size distributions that lack detailed balance and have no H-theorem.
Analysis is possible, however, through use of complex function theory
that relates Bernstein functions and complete monotonicity of densities.
In the size-discrete case, this leads to a connection between
Nevalinna-Pick functions and the Hausdorff moment problem.

For questions please contact lipschitz-pego(at)hcm.uni-bonn.de .

In case you are interested in participating, please fill out the application form. The deadline for applications is 31st May 2017. All applications, submitted after that will be considered on an individual basis.