Small data global existence for systems of wave equations: The role of asymptotics

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• Istvan Kadar (University of Cambridge)
• Tuesday 07 February 2023, 14:00-15:00
• CMS, MR13.

If you have a question about this talk, please contact Dr Greg Taujanskas.

Systems of wave equations may fail to be globally well-posed, even for small initial data. Attempts to classify systems into well-, and ill-posed categories work by identifying structural properties of the equations that can work as indicators of well-posedness. The most famous of these are the null and weak null conditions. As noted by Keir, related formulations may fail to properly capture the effect of undifferentiated terms in systems of wave equations. We show that this is because null conditions are only good for categorising behaviour close to null infinity and propose an alternative condition for semilinear equations that work for undifferentiated non-linearities as well. Furthermore, we give an example of a system satisfying the weak null condition with global ill-posedness due to undifferentiated terms.

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

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