On large potential perturbations of the Schrödinger, wave and Klein--Gordon equations

Abstract

We prove a sharp resolvent estimate in scale invariant norms of Amgon--Hörmander type for a magnetic Schrödinger operator on ${\mathbb{R}}^n$, $n\ge 3$\begin{equation*} L=-(\partial+iA)^{2}+V \end{equation*}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 $L$.

arXiv comment29 pages