Selected Topics in Fluid Dynamics

by Prof. Pierangelo Marcati (Gran Sasso Science Institute)

Monday 26 Feb 2024, 11:00 → Friday 1 Mar 2024, 16:30 Europe/Rome

Ex-ISEF/Building-Main Lecture Hall (GSSI)

 

Lecture 1 (2h)

Lagrangian description, Vorticity stream formulation, local existence, Beale - Kato - Majda theorem, recent related results 

 

Lecture 2 (2h)
 

Yudovich - Serfati theory and connected topics

 

Lecture 3 (2h)(temptative)
 

Inviscid limits, Kato criterion, Prandtl system, Caflish Sammartino, Spectral instability, Oleinik theorem for stationary Prandtl,  Masmoudi Wang and Dalibard Masmoudi results on time the dependent problem, Grenier N'guyen 3 layers analysis

 

Lecture 4 (2h) (temptative)
 

Shear flows, Shear flow between parallel plates, linearized system Squire transformation, Rayleigh operator. Rayleigh necessary condition for instability.  

Vishik, Friedlander Grenier instability results. Arnold stability theorem. Trefeheten pseudospectral analysis.  Viscous shear flows and Orr-Sommerfeld.  Ideas on inviscid damping

 

 

Schedule of the course:

February 26, 11am - 1pm, MLH;

February 27, 11am - 1pm, MLH;

February 29, 11am - 1pm, MLH;

March 1, 2:30pm - 4:30pm, MLH.

 

For those attending the lectures online, please use the following link:

https://us02web.zoom.us/j/85092747284?pwd=NkJZejNWbUZmblkvZ3ZLK3g1RHdtUT09