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We study the energy critical wave equation in 3 dimensions around a single soliton. We obtain energy boundedness (modulo unstable modes) for the linearised problem. We use this to construct scattering solutions in a neighbourhood of timelike infinity (i₊), provided the data on null infinity () decay polynomially. Moreover, the solutions we construct are conormal on a blow-up of Minkowski space. The methods of proof also extend to some energy supercritical modifications of the equation.
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István Kádár (2024) studied this question.
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