We consider hedgehog solutions in the -dimensional Skyrme model, which is an energy-supercritical problem. We introduce a new strategy to prove global well-posedness for arbitrarily large initial data.
"Global well-posedness of hedgehog solutions for the Skyrme model." Duke Math. J. 170 (7) 1377 - 1418, 15 May 2021. https://doi.org/10.1215/00127094-2020-0067