A stochastic variational approach to the viscous Camassa-Holm and Leray-alpha equations
by Guoping Liu (GFMUL and CAS)
We will give a construction of diffusions on the (infinite dimensional) group of measure-preserving homeomorphisms in the d-dimensional torus. Based on this we will present a stochastic variational principle for the Camassa-Holm equation.
Using the stochastic characterisation, we will show the existence of a weak solution subject to some particular final conditions. In the remaining time, we wish to use a different class of admissible variations to get a similar result for the Leray-alpha equation.