MTH-220.4 PDEs on Incompressible Flows

Syllabus

1. Fundamental equations for fluid dynamics equations - Eulerian and Lagrangian descriptions.
2. Incompressible Navier Stokes equations
   - Leray-Hopf weak solutions: Existence in any dimensions and uniqueness in 2D (In 3D uniqueness is open, related to one of the Clay millennium problem).
   - Caffarelli-Kohn-Nirenberg type blow-up result for suitable weak solutions of NSE.
   - Mild solutions to NSE and blow-up criterion for mild solutions: Prodi-Serrin condition (Calderón-Zygmund theory).

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