Long-time evolution of forced waves in the low viscosity regime

2025/07/31 by Frantz, Nicolas, Wrochna, Michał
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2508.00189

Abstract

We consider a model for internal waves described by a zero order pseudo-differential Hamiltonian P damped by a second order viscosity term i νQ. Under Morse-Smale or similar weaker global conditions on the classical dynamics, we describe qualitatively the long-time behavior of solutions of the corresponding evolution equation with smooth forcing in a small ν regime. We show that dissipation effects arise no earlier than at the t∼ ν^-1/3- time scale.

Citations

• Internal waves in a 2D subcritical channel
• Internal waves in aquariums with characteristic corners
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• Characterization of singular flows of zeroth-order pseudo-differential operators via elliptic eigenfunctions: a numerical study
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• The remarkable effectiveness of time-dependent damping terms for second order evolution equations