We give a sufficient condition under which the solutions of the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential blow up. The method is a modified variational approach, in the spirit of the work by Ibrahim et al. [Anal. PDE 4 (2011), 405-460].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am40-2-3, author = {Jing Lu}, title = {Blow-up for the energy-critical nonlinear wave equation and Schr\"odinger equation with inverse-square potential}, journal = {Applicationes Mathematicae}, volume = {40}, year = {2013}, pages = {183-196}, zbl = {1283.35127}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-2-3} }
Jing Lu. Blow-up for the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential. Applicationes Mathematicae, Tome 40 (2013) pp. 183-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-2-3/