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<p>We study the energy critical wave equation in three 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 (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(i_+\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>i</mi> <mo>+</mo> </msub> </math></EquationSource> </InlineEquation>), provided the data on null infinity (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {I}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">I</mi> </math></EquationSource> </InlineEquation>) decay polynomially. Moreover, the solutions we construct are conormal on a compact manifold, the interior of which is Minkowski space. The methods of proof also extend to some energy supercritical modifications of the equation.</p>

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A Scattering Theory Construction of Dynamical Solitons in 3D

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月3日

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  • Istvan Kadar

摘要

We study the energy critical wave equation in three 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 ( \(i_+\) i + ), provided the data on null infinity ( \(\mathcal {I}\) I ) decay polynomially. Moreover, the solutions we construct are conormal on a compact manifold, the interior of which is Minkowski space. The methods of proof also extend to some energy supercritical modifications of the equation.