Past lectures

Resources

Abstract

Despite dating back to the mid-​1800s the field of hydrodynamic stability is not only surprisingly vast and varied but has undergone many significant shifts and is in a phase of rapid expansion in mathematics. In these lectures we will discuss the relationship between new and classical perspectives on hydrodynamic stability and provide an introduction to recent advances and to outstanding open problems. The focus will be specifically on the linear and nonlinear dynamics near simple solutions (shear flows and vortices) of the incompressible Navier-​Stokes in the high Reynolds number limit in two and three dimensions.

This course will assume familiarity with PDEs and functional analysis, but no prior experience with the Navier-​Stokes or Euler equations will be assumed. Exposure to the spectral theory of unbounded operators would be helpful but will not be assumed.