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A scattering theory construction of dynamical solitons in 3d

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arxiv 2403.13891 v1 pith:5JNOP3EX submitted 2024-03-20 math.AP

Istvan Kadar This is my paper · ORCID
classification math.AP
keywords energyconstructequationinfinityscatteringsolutionsaroundblow-up
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abstract

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 ($\scri$) 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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  1. Stability of the catenoid for the hyperbolic vanishing mean curvature equation in 4 spatial dimensions

    math.AP 2024-11 conditional novelty 7.0 of 10

    In four spatial dimensions, small codimension-1 perturbations of catenoid initial data yield global HVMC solutions that converge modulo translation and boost to a boosted/translated catenoid with explicit decay rates.

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