Resumen de Instability of radial standing waves of Schrödinger equation on the exterior of a ball

Orlando Lopes

• Under smoothness and growth assumptions on f we show that a standing wave w(t,x)=eibtf(x) of the Schrödinger equation on the exterior W of a ball and Neumann boundary condition wt=i(Dw +f(|w|2)w) ¶w/¶n=0 on ¶W where b is real and f is real and radially symmetric, is always linearly unstable under perturbations in the space H1(W) (it may be stable under perturbations in H1rad(W)).

  The instability is independent of f having a fixed sign andof its Morse index.

  The main tool is a theorem of linearized instability of M. Grillakis.