Microlocal analysis of forced waves

Semyon Dyatlov; Maciej Zworski

doi:10.2140/paa.2019.1.359

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Home > Journals > Pure Appl. Anal. > Volume 1 > Issue 3 > Article

2019 Microlocal analysis of forced waves

Semyon Dyatlov, Maciej Zworski

Pure Appl. Anal. 1(3): 359-384 (2019). DOI: 10.2140/paa.2019.1.359

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Abstract

We use radial estimates for pseudodifferential operators to describe long-time evolution of solutions to $i u_{t} - P u = f$ , 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.