Date and Time:
April 7 (Tue), 2020, 13:00-
April 8 (Wed), 2020, 13:00-
April 10 (Fri), 2020, 14:45-
April 14 (Tue), 2020, 13:00-
April 17 (Fri), 2020, 14:45-
Venue: Room 18-02, 18th Floor, Building No. 51, Nishiwaseda Campus, Waseda University
Lecturer: Professor Franco Flandoli (Scuola Normale Superiore di Pisa, Italy)
Participants: Open to all students, faculty members, and the general public
Registration: No registration required
Lecture no. 1 April 7
Brief review of fluid mechanics, with special view to elements of interest for atmosphere-ocean models. Introduction to noise in fluid mechanics models: e.g. additive noise in heat exchange, multiplicative advection noise in moment equations due to stochastic model reduction. Outline of problems to be solved.
Lecture no. 2 April 8
Compactness method for PDEs with the variant useful for the stochastic case. Application to SDEs and to incompressible Navier-Stokes equations with noise, in dimension 2 and 3. Uniqueness in dimension 2.
Lecture n. 3 April 10
The viewpoint of random dynamical systems; pathwise solutions,
flows and random attractor; a definition of weather and climate.
Lecture n. 4 April 14
Regularization by noise: finite dimensional classical examples; some classical examples for PDEs and a recent example for the 3D Navier-Stokes equations.
Lecture n. 5 April 17
The Kolmogorov equation viewpoint to the computation of probabilities. Link with stochastic equations, some existence and uniqueness results also in infinite dimensions, numerical methods.