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Microlocal analysis of
forced waves
Semyon Dyatlov and Maciej Zworski |
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Vol. 1 (2019), No. 3, 359–384
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Abstract |
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We use radial estimates for pseudodifferential operators to describe long-time evolution of solutions to , where is a self-adjoint zeroth-order pseudodifferential operator satisfying hyperbolic dynamical assumptions and where 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. |
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Dedicated to Richard Melrose on the occasion of his 70th birthday |
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Keywords
forced waves, spectral theory, pseudodifferential
operators, radial estimates
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Mathematical Subject Classification 2010
Primary: 35A27
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Milestones
Received: 3 July 2018
Revised: 18 April 2019
Accepted: 19 April 2019
Published: 17 July 2019
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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 |
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