Speaker
Joshua Kortum
Description
In this talk, we investigate the linearized Prandtl equations around a shear flow with non-degenerate critical point. Under a separation of variable ansatz, we completely classify all separated solutions of the equation and discuss qualitative properties of the latter. The solutions of the corresponding (algebraic) eigenvalue problem can be computed by the well-known harmonic oscillator. As a consequence, we give explicit values of eigenvalues and -functions for which the linearized Prandtl equations are unstable. However, we also show that this instability cannot be prolonged a simple way outside the well-known Sobolev regime (in particular not to Gevrey spaces).
