A stochastic Burgers equation: Bringing together chaos expansion, embedding theorems, and Catalan numbers
Seminar Room 1, Newton Institute
A special stochastic perturbation of the Burgers equation is considered. The nature of the perturbation is such that the solution is not square-integrable, and the growth of the norms at different stochastic scales is described by the Catalan numbers. Many similar equations with quadratic nonlinearity exhibit the same behavior.