Spectral theory of pseudo-differential operators of degree 0 and application to forced linear waves

Abstract

We extend the results of our paper "Attractors for two dimensional waves with homogeneous Hamiltonians of degree 0" written with Laure Saint-Raymond to the case of forced linear wave equations in any dimension. We prove that, in dimension 2,if the foliation on the boundary at infinity of the energy shell is Morse-Smale, we can apply Mourre's theory and hence get the asymptotics of the forced solution. We also characterize the wavefrontsets of the limit Schwartz distribution using radial propagation estimates.

References in corpus (3)

• Quantitative laboratory observations of internal wave reflection on ascending slopes
• Axisymmetric inertial modes in a spherical shell at low Ekman numbers
• Microlocal analysis of forced waves

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