Ricerc@Sapienza

We prove a sharp resolvent estimate in scale invariant norms of Amgon–Hörmander type for a magnetic Schrödinger operator on Rn, n ≥ 3 L = −(∂ + iA)2 + V with large potentials A, V of almost critical decay and regularity. The estimate is applied to prove sharp smoothing and Strichartz estimates for the Schrödinger, wave and Klein–Gordon flows associated to L.

In this paper we study uniqueness properties of solutions to the Zakharov-Kuznetsov equation of plasma physic. Given two sufficiently regular solutions u(1), u(2), we prove that, if decays fast enough at two distinct times, then u(1) = u(2.)