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Stochastic Partial Differential Equations in Fluid Mechanics 2021

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.

Professor Franco Flandoli (Scuola Normale Superiore di Pisa, Italy)

Event details

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

Languages: English
Lecturer: Professor Franco Flandoli (Scuola Normale Superiore di Pisa, Italy)
Participants: Open to all students, faculty members, and the general public
Admission: Free

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 

■Slides :  Lecture 4 

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.

■Lecture notes:Chapter3_final  New!  

■Slides : Lecture5  New!  

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Mon, 08 Mar 2021

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