Jonathan Winghong Luk, Associate Professor

Mailing Address:
Stanford University Department of Mathematics
Building 380
Stanford, CA 94305
USA

Office: 382-Z
E-mail: jluk AT stanford DOT edu

CV

Research Interests:

Nonlinear partial differential equations, general relativity, mathematical physics

Teaching:

During Autumn 2019, I am teaching Math 61CM and Math 220/CME 303.
I have written a set of notes on nonlinear wave equations, which can be found here. It is complemented by a review on Fourier analysis and the following example sheets (1, 2, 3).
Previous teaching can be found here.

Papers and Preprints:

  1. (with C. Huneau) Trilinear compensated compactness and Burnett's conjecture in general relativity, preprint.
  2. Stability of vacuum for the Landau equation with moderately soft potentials, Annals of PDE, 5:11, 2019.
  3. (with M. Dafermos) The interior of dynamical vacuum black holes I: The C0-stability of the Kerr Cauchy horizon, preprint.
  4. (with D. Gajic) The interior of dynamical extremal black holes in spherical symmetry, Pure and Appl. Anal., 1(2):263-326, 2019.
  5. (with C. Huneau) High-frequency backreaction for the Einstein equations under polarized U(1) symmetry, Duke Math. J., 67(18):3315-3402, 2018.
  6. (with C. Huneau) Einstein equations under polarized U(1) symmetry in an elliptic gauge, Comm. Math. Phys., 361(3):873-949, 2018.
  7. (with S.-J. Oh and S. Yang) Dynamical black holes with prescribed masses in spherical symmetry, preprint.
  8. (with S.-J. Oh) Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data II. The exterior of the black hole region, Annals of PDE, 5(6), 2019.
  9. (with S.-J. Oh) Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data I. The interior of the black hole region, Annals of Math., 190(1):1-111, 2019.
  10. (with J. Speck) Shock formation in solutions to the 2D compressible Euler equations in the presence of non-zero vorticity, Invent. Math., 214(1):1-169, 2018.
  11. (with J. Speck) The hidden null structure of the compressible Euler equations and a prelude to applications, preprint.
  12. (with S.-J. Oh and S. Yang) Solutions to the Einstein-scalar-field system in spherical symmetry with large bounded variation norms, Annals of PDE, 4:3, 2018.
  13. (with J. Speck, G. Holzegel and W. W.-Y. Wong) Stable shock formation for nearly plane symmetric waves, Annals of PDE, 2:10, 2016.
  14. (with J. Sbierski) Instability results for the wave equation in the interior of Kerr black holes, J. Funct. Anal., 271(7):1948-1995, 2016.
  15. (with G. Holzegel, J. Smulevici and C. Warnick) Asymptotic properties of linear field equations in anti-de Sitter space, preprint.
  16. (with S.-J. Oh) Proof of linear instability of the Reissner-Nordström Cauchy horizon under scalar perturbations, Duke Math. J., 166(3):437-493, 2017.
  17. (with X. An) Trapped surfaces in vacuum arising from mild incoming radiation, Adv. Theo. Math. Phys., 21(1):1-120, 2017.
  18. (with R. M. Strain) Strichartz estimates and moment bounds for the relativistic Vlasov-Maxwell system, Arch. Rat. Mech. Anal., 219(1):445-552, 2016 (combined from two earlier preprints in the 2D and 2.5D cases and the 3D case).
  19. (with R. M. Strain) A new continuation criterion for the relativistic Vlasov-Maxwell system, Comm. Math. Phys., 331:1005-1027, 2014.
  20. (with S.-J. Oh) Quantitative decay rates for dispersive solutions to the Einstein-scalar field system in spherical symmetry, Analysis and PDE, 8(7):1603-1674, 2015.
  21. Weak null singularities in general relativity, Journal of AMS. 31:1-63, 2018.
  22. (with S. Klainerman and I. Rodnianski) A fully anisotropic mechanism for formation of trapped surfaces in vacuum, Invent. Math. 194(1):1-26, 2014.
  23. (with I. Rodnianski) Nonlinear interaction of impulsive gravitational waves for the vacuum Einstein equations, Cambridge Journal of Math. 5(4): 435-570, 2017.
  24. (with I. Rodnianski) Local propagation of impulsive gravitational waves, Comm. Pure and Appl. Math., 68(4):511-624, 2015.
  25. On the local existence for the characteristic initial value problem in general relativity, Int. Mat. Res. Notices, 20:4625-4678, 2012.
  26. The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes, Journal Eur. Math. Soc., 15(5):1629-1700, 2013.
  27. A vector field method approach to improved decay for solutions to the wave equation on a slowly rotating Kerr black hole, Analysis and PDE, 5(3):553-625, 2012.
  28. Improved decay for solutions to the linear wave equation on a Schwarzschild black hole, Annales Henri Poincare, 11:805-880, 2010.

Online Talks:

  • Asymptotic properties of linear field equations in anti-de Sitter space, CMO, August 2019.
  • Recent progress on the strong cosmic censorship conjecture, BHI, February 2017.
  • Interior of dynamical vacuum black holes, IHP, November 2015.
  • The stability of the Kerr Cauchy horizon and the strong cosmic censorship conjecture in general relativity, Fields Institute, June 2015.
  • Weak null singularities in general relativity, MSRI, November 2013.
  • Formation of trapped surfaces, IHP, May 2013.