The Navier-Stokes Equations

• Course Objectives – The student will understand the history, physical meaning, and contemporary challenges within the field of theoretical fluid dynamics and turbulence.
• Course Description Navier-Stokes Equations (NSE) History, derivation, physical meaning, classical solutions, stability, dynamical systems, existence, uniqueness, regularity, scales, ladder results, dissipation rates, Serrin’s blowup, capacitary approaches, mild solutions (Lebesgue, Sobolev, Besov, Morrey, BMO, Koch, Tataru), weak solutions, stochastic NSE, the Russian school, and invariant measures. (Credits 3)
• Course Pre-Requisites / Co-Requisites – EGM 6812 Fluid Dynamics I or consent of professor. An appreciation of advanced mathematics.
• Recommended Textbooks and/or Software
  • A complete set of course notes will be provided by the professor.
  • There are no required textbooks for the class.
  • Supplemental Materials – All supplementary material will be provided through the course website.