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\( - \partial_t u + \Delta u = 0 \)
The London PDE Seminar is a London-based seminar featuring speakers at the forefront of mathematical research in partial differential equations.
Upcoming Seminars
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Date/Time:
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11:00 (London time), Thursday, 13 November 2025
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Location:
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Imperial College London
Room 642; Huxley Building
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Speaker:
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Lionor Kehrberger (Max Planck Institute, Leipzig)
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Title:
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Linear and nonlinear late-time asymptotics for waves on dynamical black hole spacetimes via time integrals
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Abstract:
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In this talk, I present a robust, new method for obtaining the precise late-time asymptotics for solutions to linear and nonlinear wave equations on dynamical black hole spacetimes.
The starting point of the method is a weak quantitative stability estimate on the solution. Once this is obtained, our proof in particular uses the following insights:
1) We show that each time derivative decays one power faster: Our mechanism for proving sharp decay is then to show that sufficiently many time integrals of our initial data have finite weighted energy norms.
2) We show that by subtracting a well-chosen approximate solution, we can take an additional time integral when considering the difference, thus upgrading our sharp decay estimates to global leading-order asymptotics.
We apply this method to linear and nonlinear waves on spacetimes settling down to Schwarzschild.
The method can be extended to other geometries, and, in particular, to other spacetime dimensions (both even and odd).
Based on upcoming work with Dejan Gajic.
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Date/Time:
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11:00 (London time), Thursday, 27 November 2025
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Location:
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Imperial College London
Room 642; Huxley Building
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Speaker:
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Sam Collingbourne (University of Edinburgh)
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Organisers
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