We establish a relation between long-time strong instability and the existence (in a certain generic sense) of unbounded orbits for dynamical systems on a Banach space. We then discuss some consequences of this relation for nonlinear Schrodinger equations: Namely, we prove long-time strong instability of plane wave solutions for the cubic nonlinearity and the existence of unbounded orbits for certain nonlinearities that are close (but not quite equal) to the cubic one.
Analysis Seminar
Tuesday, November 29, 2011 - 4:30pm
Zaher Hani
Courant Institute of Mathematical Sciences, New York University