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arXiv · 1712.09935

Recurrence of singularities for second order isotropic pseudodifferential operators

Moritz Doll
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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 $H$.

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Moritz Doll. 2017-12-28. Recurrence of singularities for second order isotropic pseudodifferential operators. https://doi.org/10.1002/mana.201800034

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