Scale invariant energy smoothing estimates for the Schrödinger equation with small magnetic potential

Abstract

We consider some scale invariant generalizations of the smoothing estimates for the free Schrödinger equation obtained by Kenig, Ponce and Vega (Ann. Inst. H. Poincaré Anal. Non Lineaire 10(3) (1993), 255–288; Invent. Math. 134(3) (1998), 489–545). Applying these estimates and using appropriate commutator estimates, we obtain similar scale invariant smoothing estimates for perturbed Schrödinger equation with small magnetic potential.

Keywords

Schrödinger equation smoothing estimates magnetic potential