On the profile of energy concentration at blow-up points for sub-conformal focusing nonlinear waves

@article{Alexakis2014OnTP,
title={On the profile of energy concentration at blow-up points for sub-conformal focusing nonlinear waves},
author={S. Alexakis and A. Shao},
journal={arXiv: Analysis of PDEs},
year={2014}
}

We consider singularities of the focusing subconformal nonlinear wave equation and some generalizations of it. At noncharacteristic points on the singularity surface, Merle and Zaag have identified the rate of blow-up of the $H^1$-norm of the solution inside cones that terminate at the singularity. We derive bounds that restrict how this $H^1$-energy can be distributed inside such cones. Our proof relies on new localized estimates obtained using Carleman- type inequalities for such nonlinearâ€¦Â Expand