带特征角的水族箱内波
Internal waves in aquariums with characteristic corners
AI总结：
本研究拓展了此前针对光滑边界区域的内波研究，对带角的有效二维水族箱内波长时间传播的奇异剖面做了微局部描述，发现除对应经典动力学吸引子的奇异性外，角点还会向外传播更温和的奇异性。
摘要：
我们对有效二维水族箱内波长时间传播中形成的奇异剖面给出了精确的微局部描述。我们考虑带角的区域，例如Maas等人实验装置中出现的多边形区域。这拓展了Dyatlov–Wang–Zworski此前发表于arXiv:2112.10191的研究，该研究考虑的是光滑边界区域。我们表明，除了对应于基础经典动力学中吸引子的奇异性外，较温和的奇异性也会从角点向外传播。
英文摘要：
We give a precise microlocal description of the singular profile that forms in the long-time propagation of internal waves in an effectively two-dimensional aquarium. We allow domains with corners, such as polygons appearing in the experimental set ups of Maas et al. This extends the previous work of Dyatlov--Wang--Zworski arXiv:2112.10191, which considered domains with smooth boundary. We show that in addition to singularities that correspond to attractors in the underlying classical dynamics, milder singularities propagate out of the corners as well.
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