Seminar Analysis and Mathematical Physics: Marc Nualart (Imperial College London)

Linear Inviscid Damping in the 2D Euler-Boussinesq system in the periodic channel

In this talk we consider the long-time behavior of solutions to the two dimensional non-homogeneous Euler equations under the Boussinesq approximation posed on a periodic channel. We prove inviscid damping  for the linearized equations around the stably stratified Couette flow using stationary-phase methods of oscillatory integrals. We discuss how these oscillatory integrals arise,  what are the main regularity requirements to carry out the stationary-phase arguments, and how to achieve such regularities.

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