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Research
Central Topic:
nonlinear partial differential equations, in particular Hamiltonian dispersive PDE and Navier-Stokes.
General Interest:
analysis, probability, signal processing & stochastic differential equations
Side Projects:
interacting-particle model to simulate phenotype evolution
Blowup of Supercritical NLS on a Ring
There exist data for which the focusing cubic nonlinear Schrödinger equation in three dimensions blows up on a ring. In higher dimensions, the proof establishes blowup on a set of co-dimension two.
| To Appear, in Analysis & PDE | (full text, 604Kb) |
Blowup of Cubic NLS with Vortex Profile
In two dimensions, the focusing cubic nonlinear Schrödinger equation admits vortex solitons. In the case of spin m = 1, we prove there exists a class of data that collapse with the vortex soliton profile at the log-log rate. This suggests that the L2 mass that may be concentrated at a point during generic collapse may be unbounded. Joint work with Gideon Simpson.
| Journal of Mathematical Physics, Volume 52 |
Links
- Events at the UBC Math Department, including the PDE Seminar.
- Seminars at the Institute of Applied Math.
- Stephen Gustafson and Tai-Peng Tsai, my postdoc supervisors.
- Toronto Math Wiki, the Dispersive Wiki.
About Me
A lantern shop in Vietnam,
,
an alkaline lake and lava desert,
,
bourgainvillia,
,
enjoying a hike,
,
a completely gratuitous portrait of poutine,
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summer on the Northumberland Strait,
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wearing a canoe on my head,
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and finally an insect,
.