Program

1) PART 1: IDEAL FLUID FLOWS | Speaker: Francesco Fanelli (BCAM)

• The Euler equations and basic properties
• Strong solutions theory 
• Beale-Kato-Majda continuation criterion and application: global existence in 2-D
• More on the 2-D case: Yudovich theory and the study of vortex patches
• The case of the ideal magnetohydrodynamics: general theory in any space dimension; the 2-D case

When: from Monday 26/02 to Wednesday 20/03 (4 weeks).

Schedule:

• Monday - 10:00 - 12:00
• Wednesday - 10:00 - 12:00.

2) PART 2: VISCOUS FLOWS | Speaker: Renato Lucà (BCAM)

• The Navier Stokes equation
• Local and small data, Strong solutions in 3D
• Global Strong solutions in 2D
• Weak solutions in 3D, the Leray Theory
• Weak-Strong uniqueness criteria
• Resistive magnetohydrodynamics, basic properties
• Topological aspects of Ideal and resistive magnetohydrodynamics

When: from Monday 08/04 to Wednesday 03/05 (4 weeks).

Schedule:

• Monday - 11:00 - 13:00
• Wednesday - 11:00 - 13:00.

Note: The last lecture will be on Tuesday 30/04, 11:00 - 13:00 (Wednesday 01/05 is bank holiday)

REFERENCES:

• Robinson, Rodrigo, Sadowski: \"The 3 dimensional Navier-Stokes equation\".
• Bertozzi, Majda: \"Vorticity and Incompressible Flow\".
• Bahouri, Chemin, Danchin: \"Fourier analysis and nonlinear partial differential equations\".