Sung-Jin Oh
University of California-Berkeley, CA·Mathematics & Statistics·Early-career
Many laws of physics, from electromagnetism and fluids to plasmas and gravity, are written as nonlinear partial differential equations (PDEs). These equations describe how quantities change in space and time, and in nonlinear ones the effects feed back on themselves.
- Fields
Mathematics & Statistics
Physics
- Topics
partial differential equations
nonlinear dispersive equations
hyperbolic equations
- Grants
- 2 known grants, through Jun 2028
What they work on
- Prove a forward-in-time scattering criterion for initially outgoing solutions of the energy-critical wave maps and hyperbolic Yang-Mills equations, as a step toward the soliton resolution conjecture in the one-soliton regime.
- Develop a Fourier-based approach that rigorously justifies sharp late-time behavior of linear and nonlinear waves along a black hole event horizon, as a starting point for studying instability of the Kerr Cauchy horizon.
- Establish a general local well-posedness theory for the Hall-magnetohydrodynamics equations of plasma physics, complementing the PI's earlier proof of ill-posedness near the trivial solution.
- Make direct progress on the Strong Cosmic Censorship conjecture for perturbations of subextremal Kerr black holes in the Einstein vacuum equation, using a recent technique for computing generic late-time tails.
- Prove asymptotic stability of the equivariant B = 1 Skyrmion in the Skyrme model, adapting methods from the PI's work on asymptotic stability of the 3-dimensional catenoid.
- Attack the soliton resolution conjecture along a sequence of times, without symmetry assumptions, for critical semilinear geometric dispersive equations, and describe typical dynamics more precisely under symmetry.
- Use degenerate dispersion, the instability mechanism behind ill-posedness of Hall-MHD, to establish enhanced or anomalous dissipation in the dissipative Hall-magnetohydrodynamics equations.
More about the research
Two important families are hyperbolic equations, which describe waves, and dispersive equations, in which waves spread out as they travel. The research proves rigorous theorems about three kinds of questions. What do solutions look like after a very long time? Can they form singularities? Are special solutions stable or unstable? The equations come from general relativity, particle field theories and plasma physics, and the two projects share several long-running targets.
Why it matters
This is pure mathematics. It adds rigorous proofs about how solutions to fundamental physics equations behave over long times and when they form singularities. These results could clarify strongly nonlinear phenomena such as singularities inside black hole spacetimes, the formation and stability of solitons, and small-scale structure, dissipation and magnetic reconnection in plasmas.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Peter Hintz
Pennsylvania State University, PA·Mathematics & Statistics
Prove nonlinear stability of Kerr black holes, the standard model of a rotating black hole, for all spins below the maximum, showing that small disturbances decay over time, using geometric and microlocal analysis of wave equations.
Andrew Lawrie
University of Maryland, MD·Mathematics & Statistics
Work toward proving the soliton resolution conjecture, which predicts that generic solutions split into finitely many solitons plus radiation, without symmetry assumptions, beginning with the harmonic map heat flow in two dimensions.
Sergiu Klainerman
Princeton University, NJ·Mathematics & Statistics
Work toward proving the nonlinear stability of Kerr black holes with large angular momentum, removing the main obstacle to extending known results for slowly rotating black holes.
The school
University of California-Berkeley: 46 labs on PI Pages, $1.1B a year on research, 825 research doctorates a year.
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