| Talk_id | Date | Speaker | Title |
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16478
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Wednesday 2/6
4:10 PM
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Mihai Tohaneanu, University of Kentucky
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Local energy estimates on black hole backgrounds
- Mihai Tohaneanu, University of Kentucky
- Local energy estimates on black hole backgrounds
- 02/06/2019
- 4:10 PM - 5:00 PM
- C517 Wells Hall
Local energy estimates are a robust way to measure decay of solutions to linear wave equations. I will discuss several such results on black hole backgrounds, such as Schwarzschild, Kerr, and suitable perturbations converging at various rates, and briefly discuss applications to nonlinear problems. The most challenging geometric feature one needs to deal with is the presence of trapped null geodesics, whose presence yield unavoidable losses in the estimates. This is joint work with Lindblad, Marzuola, Metcalfe, and Tataru.
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17490
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Wednesday 2/13
4:10 PM
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Albert Ai, UC Berkeley
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Low Regularity Solutions for Gravity Water Waves
- Albert Ai, UC Berkeley
- Low Regularity Solutions for Gravity Water Waves
- 02/13/2019
- 4:10 PM - 5:00 PM
- C517 Wells Hall
We consider the local well-posedness of the Cauchy problem for the gravity water waves equations, which model the free interface between a fluid and air in the presence of gravity. It has been known that by using dispersive effects, one can lower the regularity threshold for well-posedness, below that which is attainable by energy estimates alone. This program was initiated for gravity water waves by Alazard-Burq-Zuily, by proving Strichartz estimates with loss. We discuss how these Strichartz estimates, and thus the low regularity threshold, can be sharpened by applying an integration along the Hamilton flow combined with local smoothing estimates.
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17491
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Wednesday 3/13
4:10 PM
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Jonas Lührmann, Johns Hopkins
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Local smoothing estimates for Schrödinger equations on hyperbolic space and applications
- Jonas Lührmann, Johns Hopkins
- Local smoothing estimates for Schrödinger equations on hyperbolic space and applications
- 03/13/2019
- 4:10 PM - 5:00 PM
- C517 Wells Hall
We establish frequency-localized local smoothing estimates for Schrödinger equations on hyperbolic space. The proof is based on the positive commutator method and a heat flow based Littlewood-Paley theory. Our results and techniques are motivated by applications to the problem of stability of solitary waves to nonlinear Schrödinger-type equations on hyperbolic space.
The talk is based on joint work with Andrew Lawrie, Sung-Jin Oh, and Sohrab Shahshahani.
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17492
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Wednesday 3/27
4:10 PM
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Yash Jhaveri, Institute for Advanced Study
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TBA
- Yash Jhaveri, Institute for Advanced Study
- TBA
- 03/27/2019
- 4:10 PM - 5:00 PM
- C517 Wells Hall
No abstract available.
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