Justin Holmer

Brown Univ. Math. Dept.
Box 1917
151 Thayer Street
Providence, RI 02912 		Email: holmer@math.brown.edu
Office: 210 Kassar-Gould House
Phone: (401) 863-1123
Fax: (401) 863-9013

I am an assistant professor in the Department of Mathematics at Brown University.

This semester I am the math department colloquium organizer. Here is the colloquium schedule.

Courses

Papers/Preprints

  • (with Rodrigo Platte and Svetlana Roudenko) Blow-up criteria for the 3d cubic nonlinear Schroedinger equation , preprint. pdf

  • (with Svetlana Roudenko) Divergence of infinite-variance nonradial solutions to the 3d NLS equation , preprint. pdf

  • (with I. Bejenaru, S. Herr, and D. Tataru) On the 2d Zakharov system with L^2 Schroedinger data, Nonlinearity 22 (2009) pp. 1063--1089. pdf

  • (with Maciej Zworski) Breathing patterns in nonlinear relaxation, Nonlinearity 22 (2009) pp. 1259--1301. pdf

  • (with Maciej Zworski) Geometric structure of NLS evolution, unpublished. pdf

  • (with Nikos Tzirakis) Asymptotically linear solutions in H^1 of the 2-d defocusing nonlinear Schroedinger and Hartree equations, to appear in Journal of Hyperbolic Differential Equations. pdf

  • (with Kiril Datchev) Fast soliton scattering by attractive delta impurities, to appear, Commun. Partial Differential Equations. pdf

  • (with Thomas Duyckaerts and Svetlana Roudenko) Scattering for the non-radial 3d cubic nonlinear Schroedinger equation, Math. Res. Lett. 15 (2008) pp. 1233--1250. pdf

  • (with Maciej Zworski) Soliton interaction with slowly varying potentials, IMRN Internat. Math. Res. Notices 2008 (2008), Art. ID runn026, 36 pp. pdf

  • (with Svetlana Roudenko) A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation, Comm. Math. Phys. 282 (2008) pp. 435--467. pdf.
    We have an unpublished erratum that corrects an improper use of the Strichartz estimates in S 2.

  • (with Svetlana Roudenko) On blow-up solutions to the 3d cubic nonlinear Schroedinger equation, AMRX Appl. Math. Res. Express 2007 (2007), Art. ID abm004, 29 pp. pdf

  • (with Maciej Zworski) Slow soliton interaction with delta impurities, J. Modern Dynamics 1 (2007), pp. 689--718. pdf.

  • (with J. Colliander, M. Visan, and X. Zhang) Global existence and scattering for rough solutions to generalized nonlinear Schroedinger equations on R, Commun. Pure Appl. Anal. 7 (2008), no. 3, pp. 467--489. pdf.

  • (with Jeremy Marzuola and Maciej Zworski) Soliton splitting by external delta potentials, J. Nonlinear Science 17 (2007), pp. 349-367. pdf.
    This is a numerical companion to our paper, Fast soliton scattering by delta impurities, posted below.

  • (with James Colliander and Nikolaos Tzirakis) Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schroedinger systems, to appear, Trans. Amer. Math. Soc. pdf.

  • Local ill-posedness of the 1d Zakharov system, Electron. J. Differential Equations, Vol. 2007(2007), No. 24, pp. 1-22. pdf

  • (with Jeremy Marzuola and Maciej Zworski) Fast soliton scattering by delta impurities, Comm. Math. Phys. 274 (2007), pp. 187-216. pdf

  • The initial-boundary value problem for the Korteweg-de Vries equation, Comm. Partial Differential Equations 31 (2006), pp. 1151-1190. pdf

  • The initial-boundary value problem for the 1d nonlinear Schroedinger equation on the half-line, Differential Integral Equations 18 (2005), pp. 647-668. pdf

  • Ph.D. Thesis, University of Chicago, 2004. Uniform estimates for the Zakharov system and the initial-boundary value problem for the Korteweg-de Vries and nonlinear Schroedinger equations. 210 pages. pdf. Ph.D. Thesis summary. 10 pages. pdf.

Other Materials

  • Lecture notes for the Park City Math Institute graduate summer school course "The Cauchy problem for the Quasilinear Schrodinger equation," delivered by Carlos Kenig, July 13-18, 2003. These notes are authored by Carlos Kenig. Revised June 2005, 125 pages. pdf.