Vol. 1, No. 3, 2019

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Microlocal analysis of forced waves

Semyon Dyatlov and Maciej Zworski

Vol. 1 (2019), No. 3, 359–384
Abstract

We use radial estimates for pseudodifferential operators to describe long-time evolution of solutions to iut Pu = f, where P is a self-adjoint zeroth-order pseudodifferential operator satisfying hyperbolic dynamical assumptions and where f is smooth. This is motivated by recent results of Colin de Verdière and Saint-Raymond (2019) concerning a microlocal model of internal waves in stratified fluids.

Dedicated to Richard Melrose on the occasion of his 70th birthday

Keywords
forced waves, spectral theory, pseudodifferential operators, radial estimates
Mathematical Subject Classification 2010
Primary: 35A27
Milestones
Received: 3 July 2018
Revised: 18 April 2019
Accepted: 19 April 2019
Published: 17 July 2019
Authors
Semyon Dyatlov
Department of Mathematics
University of California
Berkeley, CA
United States
Department of Mathematics
MIT
Cambridge, MA
United States
Maciej Zworski
Department of Mathematics
University of California
Berkeley, CA
United States