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Slow blow-up solutions for the H^1(R^3) critical focusing semi-linear wave equation in R^3

Joachim Krieger·Wilhelm Schlag·Daniel Tataru
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Abstract

We prove the existence of energy solutions of the energy critical focusing wave equation in R^3 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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Joachim Krieger, Wilhelm Schlag, Daniel Tataru. 2007-02-01. Slow blow-up solutions for the H^1(R^3) critical focusing semi-linear wave equation in R^3. https://arxiv.org/abs/math/0702033

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