Recurrence of singularities for second order isotropic pseudodifferential operators

Abstract

Let $H$ be a self-adjoint isotropic elliptic pseudodifferential operator of order $2$. Denote by $u(t)$ the solution of the Schrödinger equation $(i{\partial }_t-H)u=0$ with initial data $u(0)=u_0$. If $u_0$ is compactly supported the solution $u(t)$ is smooth for small $t>0$, but not for all $t$. We determine the wavefront set of $u(t)$ in terms of the wavefront set of $u_0$ and the principal and subprincipal symbol of $H$.

19 pages

References in corpus (1)

• Refined Weyl law for homogeneous perturbations of the harmonic oscillator