Publication

Nonscattering solutions and blowup at infinity for the critical wave equation

Joachim Krieger, Roland Donninger
2013
Journal Articles

Abstract

We consider the critical focusing wave equation (−∂2t+Δ)u+u5=0 in R1+3 and prove the existence of energy class solutions which are of the form u(t,x)=tμ2W(tμx)+η(t,x) in the forward lightcone {(t,x)∈R×R3:|x|≤t,t≫1} where W(x)=(1+13|x|2)−12 is the ground state soliton, μ is an arbitrary prescribed real number (positive or negative) with |μ|≪1 , and the error η satisfies ∥∂tη(t,⋅)∥L2(Bt)+∥∇η(t,⋅)∥L2(Bt)≪1,Bt:={x∈R3:|x|

Official source

https://infoscience.epfl.ch/entities/publication/27d4a020-5cc5-441d-9daa-5c081ec1e712

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Nonscattering solutions and blowup at infinity for the critical wave equation

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