Microlocal Structures of Internal Waves in a 2D Aquarium
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li-zhenhaoli-mathematics-phd-2026.pdf
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7.82 MB
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ba6ca7e6c1b2f67f40658af641fefe93
Author(s)
Li, Zhenhao
Advisor(s)
Dyatlov, Semyon
Date Issued
May 2026
Publisher
Massachusetts Institute of Technology
Abstract
We study a model of forced internal waves in an effectively two-dimensional aquarium. In bounded domains, we provide a precise microlocal description of the singular profile that forms during the long-time propagation of internal waves when the underlying classical dynamics feature attractors. By allowing for domains with corners, our model aligns with the experimental setups of Maas et al. [1]. We discover additional mild singularities that propagate from these corners. On the other hand, we show that forced internal waves remain bounded in energy when the underlying classical dynamics are sufficiently chaotic. Beyond bounded aquaria, we also consider internal waves in a channel with subcritical bottom topography. We construct the scattering matrix for the internal waves problem in a channel with straight ends, mapping incoming data to outgoing data. Furthermore, we study the long-time evolution of internal waves in these channels and show that the leading profiles of the solutions are the outgoing solutions of the stationary equation.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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