Slow blow-up solutions for the H¹(R³) critical focusing semi-linear wave equation in R³

2007/02/01 by Krieger, Joachim, Schlag, Wilhelm, Tataru, Daniel
#35L05 #35Q51 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.math/0702033

Abstract

We prove the existence of energy solutions of the energy critical focusing wave equation in R³ which blow up exactly at x=t=0. They decompose into a bulk term plus radiation term. The bulk is a rescaled version of the stationary "soliton" type solution of the NLW. The construction depends crucially on the renormalization procedure of the "soliton" which we introduced in our companion paper on the wave map problem.

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