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A stochastic variational approach to the viscous Camassa-Holm and Leray-alpha equations

GFM seminar

Dep. Matemática FCUL, sala 6.2.33

2015-12-02 15:00 .. 16:00

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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.

Past conference highlights: Symmetries in Quantum Physics 2017; Advances in Mathematical Fluid Mechanics, Stochastic & Deterministic Methods; Quantum Integrable Systems and Geometry; Chern-Simons Gauge Theory: 20 years after; Second Workshop on Quantum Gravity and Noncommutative Geometry; Infinite Dimensional Algebras and Quantum Integrable Systems II; Stochastic Analysis in Mathematical Physics; Mathematics in Chemistry; Geometric Aspects of Integrable Systems; ICMP 2003