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Creators/Authors contains: "Lawrie, Andrew"

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  1. ; ; (, Forum of Mathematics, Pi)
    Abstract We consider the harmonic map heat flow for maps$$\mathbb {R}^{2} \to \mathbb {S}^2$$. It is known that solutions to the initial value problem exhibit bubbling along a well-chosen sequence of times. We prove that every sequence of times admits a subsequence along which bubbling occurs. This is deduced as a corollary of our main theorem, which shows that the solution approaches the family of multi-bubble configurations in continuous time. 
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    Free, publicly-accessible full text available January 1, 2026
  2. ; (, Journal of the American Mathematical Society)
    We consider the equivariant wave maps equation R 1 + 2 →<#comment/> S 2 \mathbb {R}^{1+2} \to \mathbb {S}^2 , in all equivariance classes k ∈<#comment/> N k \in \mathbb {N} . We prove that every finite energy solution resolves, continuously in time, into a superposition of asymptotically decoupling harmonic maps and free radiation. 
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    Free, publicly-accessible full text available December 3, 2025
  3. ; (, Annals of PDE)
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  4. ; ; (, Duke Mathematical Journal)
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  5. ; (, Annals of PDE)
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  6. ; ; ; (, Analysis & PDE)
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  7. ; (, Inventiones mathematicae)
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  8. ; ; (, Physical Review E)
  9. ; ; ; (, Advances in Mathematics)
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  10. ; ; (, Geometric and Functional Analysis)
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