Microlocal analysis of forced waves
Copyright policy )Microlocal analysis of forced waves
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 0th order pseudodifferential operator satisfying hyperbolic dynamical assumptions and where $ f $ is smooth. This is motivated by recent results of Colin de Verdi��re and Saint-Raymond [arXiv:1801.05582] concerning a microlocal model of internal waves in stratified fluids.
27 pages, 4 figures; minor changes. To appear in Pure and Applied Analysis
- University of California, San Francisco United States
- University of California System United States
- University of California
- Department of Mathematics University of California (UCLA) University Park United States
- University of California Finland
Mathematics - Analysis of PDEs, Initial value problems for PDEs with pseudodifferential operators, forced waves, FOS: Mathematics, spectral theory, pseudodifferential operators, long-time evolution, 35A27, Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs, radial estimates, Analysis of PDEs (math.AP)
Mathematics - Analysis of PDEs, Initial value problems for PDEs with pseudodifferential operators, forced waves, FOS: Mathematics, spectral theory, pseudodifferential operators, long-time evolution, 35A27, Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs, radial estimates, Analysis of PDEs (math.AP)
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