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ACMS Abstracts: Spring 2015

Irene Kyza (U Dundee)

Semiclassical regularization for ill-posed classical flows: microlocal coarse-graining beyond Wigner measures

Wigner measures (WMs) have been successfully used as a parameter-free tool to provide homogenised descriptions of wave problems. Notable applications are the efficient simulation of large linear wave fields, and the painless resolution of linear caustics. However, their applicability to non-linear problems has been very limited.

In this talk we discuss the role of smoothness of the underlying flow as a limiting factor in the applicability of WMs. Non-smooth flows are ill-posed for measures, and new phenomena are possible in that regime. For example, single wavepackets may be "split" cleanly into several new wavepackets. We introduce a modification of the WM approach, and show that it can capture successfully some of these new phenomena. These results include joint work with T. Paul, I. Kyza and Th. Katsaounis.

The main idea behind this regularised scheme can be used to setup a unifying framework for several different approaches developed in the last few years. Some ideas about the extension of this framework to non-linear problems are also discussed.