Conditional global existence and scattering for a semi-linear Skyrme equation with large data

Andrew Lawrie

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arXiv · 1311.0901

Conditional global existence and scattering for a semi-linear Skyrme equation with large data

Andrew Lawrie

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Abstract

We study a generalization of energy super-critical wave maps due to Adkins and Nappi that can also be viewed as a simplified version of the Skyrme model. These are maps from 1+3 dimensional Minkowski space that take values in the 3-sphere, and it follows that every finite energy Adkins-Nappi wave map has a fixed topological degree which is an integer. Here we initiate the study of the large data dynamics for Adkins-Nappi wave maps by proving that there is no type II blow-up in the class of maps with topological degree zero. In particular, any degree zero map whose critical norm stays bounded must be global-in-time and scatter to zero as time tends to infinity.

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Andrew Lawrie. 2013-11-20. Conditional global existence and scattering for a semi-linear Skyrme equation with large data. https://arxiv.org/abs/1311.0901

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