ShowMe Analysis Meeting 2004 June 3-5, 2004 University of Missouri Columbia, Missouri

Atanas Stefanov (University of Kansas)
Strichartz estimates for the Schroedinger equation with small magnetic field

Abstract: We will consider the linear Schroedinger equation with small time dependent magnetic field. We show that under appropriate smallness condition on the magnetic potential the associated linear evolution propagator satisfy energy and optimal decay estimates, which in turn imply the optimal range of the Strichartz estimates. As an application, we show the global well-posedness for small data of semilinear Schroedinger equation in the presence of (small) magnetic field.