Attractors for two dimensional waves with homogeneous Hamiltonians of degree 0

2018/01/16 by Yves Colin de Verdìère, de Verdìère, Yves Colin, Laure Saint‐Raymond +3 · 3 citations
Computer Science · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Classical Physics (physics.class-ph) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Nonlinear Dynamics and Pattern Formation #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1801.05582

openalex publication_date 2018/01/17 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28

Abstract

The density stratification in an incompressible fluid is responsible for the propagation of internal waves. In domains with topography, these waves exhibit interesting features. In particular, numerical and lab experiments show that, in two dimensions, for generic forcing frequencies, these waves concentrate on attractors. The goal of this paper is to analyze mathematically this behavior, using tools from spectral theory and microlocal analysis. The same results apply also to inertial waves in rotating fluids.

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