Well-posedness of weakly hyperbolic systems of PDEs in Gevrey regularity.

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• Baptiste Morisse, University of Cardiff
• Monday 12 February 2018, 15:00-16:00
• CMS, MR13.

If you have a question about this talk, please contact Josephine Evans.

I consider systems of first-order PDEs, which are weakly hyperbolic: the spectrum of the principal symbol is real but eigenvalues may cross. Close to one of those crossing eigenvalues, lower order linear terms may induce a typical Gevrey growth in frequency. I will present an energy estimate in Gevrey regularity, using an approximate symmetrizer of the principal symbol. The symbol of such an approximate symmetrizer is in a special class of symbols, related to a specific metric in phase space. For such symbols, composition of associated operators lead to error terms that only can be handle thanks to the Gevrey energy.

This talk is part of the Partial Differential Equations seminar series.

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