Title: “Mathematical analysis of incompressible flow”

Prof. Milton C. Lopes Filho (UFRJ)

Description: This is na advanced course in PDE, which assumes a working knowledge of basic PDE at the level of L. C. Evans’ book.

Classes: Tuesdays and Fridays, 10:30-12:00, IMPA, Room 347.

Begins: March 11, 2014.

Syllabus:

• Derivation of the equations of Euler and Navier-Stokes;
• Symmetries and conserved quantities;
• Vorticity;
• Classical solutions, existence and uniqueness;
• Singularities, Beale-Kato-Majda;
• Weak solutions, vortex sheets, wild solutions;
• Boundary layers, Kato criterion;
• Turbulence;

References:

• A. Majda and A. Bertozzi – Vorticity and the Mathematical Theory of Incompressible Fluid Flow
  
  
• M. C. Lopes Filho, H. J. Nussenzveig Lopes and Y. Zheng - Weak solutions of the equations of incompressible and inviscid fluid dynamics