Friday, July 28, 2017 - 10:15 in T2-228
Statistical solutions of evolution equations and selection of measurable semiflows
A talk in the Bielefeld Stochastic Afternoon series by
Jorge Cardona from University of Miami
| Abstract: |
In this talk, I will present a general result on the existence of measurable selections with the semigroup property (measurable semiflow). Then, I will review some statistical solutions for evolution equations. In particular, the Hopf statistical solutions, the Foias statistical solutions, and Vishik-Fursikov measures. I will present a new type of statistical solutions: the Markov statistical solutions. I will use a simple ODE with non-uniqueness and the nonlinear Schrodinger equation with power-like nonlinearity as test cases for the existence of such type of solutions. In the last part, I will present a slight variation to the Markov selection theorem as presented by Flandoli and Romito.
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