Professor Franco Flandoli from the Scuola Normale Superiore di Pisa in Italy will give a series of lectures on the stochastic partial differential equations in fluid mechanics.
Date and Time:
April 8 (Thurs.), 2021 from 16:00-18:20
April 15 (Thurs.), 2021 from 16:00-18:20
April 22 (Thurs.), 2021 from 16:00-18:20
April 29 (Thurs.), 2021 from 16:00-18:20
May 6 (Thurs.), 2021 from 16:00-18:20
Venue: Real-time Zoom lectures ⇒Registration
Lecturer: Professor Franco Flandoli (Scuola Normale Superiore di Pisa, Italy)
Participants: Open to all students, faculty members, and the general public
Lecture no. 1 April 8 (Thurs.)
Stochastic Navier-Stokes equations with additive noise in dimension 2 and 3: basic definitions, path by path approach. Hint to the random dynamical system viewpoint.
■Lecture notes： Chapter 1
■Slides : Lecture 1
Lecture no. 2 April 15 (Thurs.)
Stochastic Navier-Stokes equations in dimension 2 and 3 with more general noise, including transport type one: compactness method, weak solutions; uniqueness in dimension 2. Hint to the problem of Markov selections in dimension 3.
■Lecture notes： Chapter 2 (Half version)
■Slides : Lecture 2
Lecture no. 3 April 22 (Thurs.)
Navier-Stokes equations with Stratonovich transport type noise: basic definitions, conservation laws. Intuition about its emergence from model reduction; a rigorous proof for 2D Euler equations.
■Lecture notes： Chapter 2 (Full version)
■Slides ：Lecture 3
Lecture no. 4 April 29 (Thurs.)
Eddy viscosity and eddy dissipation produced by transport type noise; stochastic mixing and dissipation enhancement.
■Lecture notes ：Chapter 3 New!
■Slides : Lecture 4 New!
Lecture no. 5 May 6 (Thurs.)
Regularization by noise: results and open problems concerning transport equations, Euler and Navier-Stokes equations with transport type noise.