Microlocal analysis of forced waves

Abstract

We use radial estimates for pseudodifferential operators to describe long time evolution of solutions to $i{u}_t-Pu=f$ 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 Verdière and Saint-Raymond [arXiv:1801.05582] concerning a microlocal model of internal waves in stratified fluids.

arXiv comment27 pages, 4 figures; minor changes. To appear in Pure and Applied Analysis

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Cited by in corpus (11)

• Spectral theory of pseudo-differential operators of degree 0 and application to forced linear waves
• Complex powers of the wave operator and the spectral action on Lorentzian scattering spaces
• Viscosity limits for 0th order pseudodifferential operators
• Space-time statistics of a linear dynamical energy cascade model
• Numerical simulations of a stochastic dynamics leading to cascades and loss of regularity: applications to fluid turbulence and generation of fractional Gaussian fields
• Equivalence of classical and quantum completeness for real principal type operators on the circle
• Mathematics of internal waves in a 2D aquarium
• Internal waves in 2D domains with ergodic classical dynamics
• Internal waves in aquariums with characteristic corners
• Eigenvalue asymptotics for polynomially compact pseudodifferenial operators and applications
• Dynamical Fractional and Multifractal Fields