Walter Craig

Canada Research Chair of Mathematical Analysis and its Applications

Department of Mathematics and Statistics, McMaster University

Department of Mathematics and Statistics
McMaster University
Hamilton, Ontario, L8S 4K1
(905) 525 9140 x23422
(905) 522 0935 (fax)
Office: Hamilton Hall 418
AIMS Laboratory, McMaster University
(905) 525 9140 x24411
Hamilton Hall 403

Department of Mathematics and Statistics homepage

Course schedule: 2017-18 Semester 2
Mathematics 4FT/6FT: Topics in Partial Differential Equations
Class: M & Th 13:30 - 15:00 in HH 312
Office Hours: F 10:30 - 12:00 or by appointment

Selected Seminar Presentations: 

        Bounds on Kolmogorov spectra for the Navier - Stokes equations,
          CMS - SMF Joint meeting,    Montreal, June 5, 2008

        Nonlinear Water Waves in Random Bathymetry,
          2007 SIAM Conference on Analysis of PDE
          December 10-12, 2007,     Mesa, Arizona

        Invariant tori for Hamiltonian PDE,
          Peking University, Beijing      August 13, 2007

        On the singular set of the Navier - Stokes equations ,
          Session on Variational problems, Joint CMS / SMM Meeting,
          Guanajuato, Mexico, September 22, 2006

        Tsunamis and ocean waves, AAAS Annual Meeting, Feb 19, 2006
              Symposium on tsunamis: their hydrodynamics and their impact on people.

        Solitary water wave interactions,
ICMS - Edinburgh, December 15, 2005

        On the Boltzmann equation, University of Michigan Oct. 5, 2005
                                                                   CRM Mathematics Colloquium Nov. 11, 2005
                                                                    beamer .pdf file

        The mathematics of ocean waves
          Pan-American Advanced Studies Institute,
          Santiago Chile, January 10 and 11, 2005
                         1: Water waves and tsunamis directory_cd1 (slides)   (part 1) (part 2)
                     2: On solitary wave interactions
directory_cd2 (slides) (part 1) (part 2)

Research interests: partial differential equations and dynamical systems

Journal editorships:

  AMS, Mathematical Surveys and Monographs;  February 1 2018 - January 31 2022.

  Communications in Contemporary Mathematics;  2006 - present.

  Complex Analysis and its Synergies;  2014 - present.

  Electronic Research  Announcements in Mathematical Sciences; (ERA-MS) February 15 2007 - February 1 2019.

  Fields Institute, Editorial Board;   2001 - present.

  Journal of Dynamics and Differential Equations;  2006 - present.

  Mathematical Reports of the Royal Society of Canada;   2008 - present.

  Nonlinear Differential Equations and Applications;  2008 - present.

Journal editorships (past):

   London Mathematical Society Monographs, 2004 - 2008.            

   Philosophical Transactions of the Royal Society - A:   January 2009 - December 2011.

   Proceedings of the AMS   Feb. 2005 - Jan. 2013.

   Mathematical Physics Electronic Journal,   2002 - 2015

   AMS, Graduate Studies in Mathematics   Feb. 2002 - Jan. 2008.

   Canadian Mathematical Society, Journal and Bulletin   2002 - 2007.

  Proceedings of the Royal Society - A:   2002 - 2008. (Proc. R. Soc A)

   SIAM: Mathematical Analysis   1998 - 2004.

Curriculum Vitae: cv.pdf file

Selected recent papers:

[107] ''On the Hamiltonian for water waves'',
Proceedings of the RIMS Symposium on Mathematical Analysis of Fluid and Gas Dynamics,
(2016) Research Inst. Math. Sciences - Kyoto, Kokyuroku.

[104] ''Mapping properties of normal forms transformations for water waves''
(with C. Sulem), Bollettino dell'Unione Matematica Italiana 9 (2016),
DOI: 10.1007/s40574-016-0078-9, pp. 289-318.

[102] ''Standing waves in near-parallel vortex filaments'',
(with C. Garcia - Azpeitia and C.-R. Yang), Commun. Math. Phys. 350 (2017) pp. 175-203.

[101] ''Normal forms transformations for capillary-gravity water waves'',
(with C. Sulem), Fields Institute Communications 75 (2015),
eds P. Guyenne, D. Nicholls and C. Sulem,
DOI: 10.1007/978-1-4939-2950-4.

[100] ''On the initial value problem for the wave equation in Friedmann - Robertson - Walker space-times'',
(with B. Abbasi), (2014) Proceedings Royal Society - A 470 20140361.

[97] ''Birkhoff normal form for the nonlinear Schroedinger equation'',
(with A. Selvitella and Y. Wang), (2013)
Rendiconti Accad. Lincei (9) Mat. Appl. 24215-228.

[95] ''The surface signature of internal waves'' (with P. Guyenne and C. Sulem),
Journal of Fluid Mechanics 710 (2012) pp. 277-303.

[93] ''Water waves over a rough bottom in the shallow water regime'' (with D. Lannes and C. Sulem),
Annales IHP - Analyse Nonlineaire 29, (2012) 233-259. 10.1016/j.anihpc.2011.10.004.

[86] ''On the size of the Navier - Stokes singular set'' (with M. Arnold),
DCDS 23 no. 8 (2010).

[79] ``Bounds on Kolmogorov spectrum for the Navier - Stokes equations'',
(with A. Biryuk), Physica D (2012). pdf-file

[78] ``Towards a new proof of Anderson localization'', (with R. Brandenberger),
archived on ArXiv-0805.4217 hep-th (2008). pdf-file

[77] ``Long wave expansions for water waves over random topography'',
(with A. deBouard, O. Diaz-Espinosa, P. Guyenne and C. Sulem)
submitted to Nonlinearity (2008). pdf-file

[75] Hamiltonian dynamical systems and applications (W. Craig, editor),
Proceedings of the Advanced Study Institute on Hamiltonian Dynamical Systems and Applications,
NATO Science for Peace and Security Series B: Springer - Verlag, (2008) XVI, 441~pp.

   in which appears

[76] ``Transformation theory of Hamiltonian PDE and the problem of water waves'',
Proceedings of the Advanced Study Institute on Hamiltonian Dynamical Systems and Applications,
NATO Science for Peace and Security Series B: Springer - Verlag, (2008), pp. 67-83. pdf-file

The following is a selection of earlier papers.

[72] Electron screening in nanostructures,
(with A. Achoyan, S. Petrosian, H. E. Ruda and A. Shik)
Journal Appl. Phys. 101 104308 (2007), and
Virtual Journal of Nanoscale Science & Technology}, June 4, 2007.

[71] Hamiltonian formulation and long wave models for
internal waves', (with P. Guyenne and H. Kalisch),
Proceedings of OMAE07, 26th International Conference on Offshore
Mechanics and Artic Engineering (2007).

[70] Construction of suitable weak solutions of the Navier - Stokes equations, pdf-file
(with A. Biryuk and S. Ibrahim), Contemp. Math 429 (2006), AMS.

[69] Mathematical aspects of surface water waves, pdf-file
Russian Math. Surveys (2007), in a collection of articles
written by speakers at the Workshop on mathematical hydrodynamics,
Steklov Institute Moscow June 2006.

[68] Surface water waves and tsunamis, pdf-file
J. Dynamics and Differential Equations 18 (2006).

[67] Solitary water wave interactions,
ICMS Workshop on Rogue Waves, December 15, 2005. pdf-file

[66] On the regularity of the Neumann problem for free
surfaces with surface tension, (with A.-M. Matei),
Proceedings AMS 135 (2006).

[65] Stable three-dimensional waves of nearly permanent form
on deep water, (with D. Henderson, M. Oscamou and H. Segur),
Mathematics and Computers in Simulation 74 (2007).

[64] Strong solutions of the Boltzmann equation in
one spatial dimension, (with A. Biryuk and V. Panferov),
C. R. Acad. Sci. Paris  - Mathématiques 342 (2006).

[63] ``Solitary wave interactions'',
(with P. Guyenne, J. Hammack, D. Henderson and C. Sulem),
Physics of Fluids 18 (2006). pdf-file

[62] ``The mathematics of thermal diffusion shocks'',
(with V. Gusev, R. LiVoti, S. Danworaphong and G. Diebold),
 Physical Review E (2005). pdf-file

[61] ``Invariant tori for Hamiltonian PDE'',
Nonlinear Dynamics and Evolution Equations,
editors: Hermann Brunner, Xiao-Qiang Zhao and Xingfu Zou,
Fields Institute Communications, AMS (2005). pdf-file

[60] ``Hamiltonian long wave expansions for free surfaces and interfaces'',
(with P. Guyenne and H. Kalisch), CPAM (2005). pdf-file

[59] ``Thermal Diffusion Shock Waves'',
(with S. Danworaphong, V. Gusev and G. Diebold)
Phys. Rev. Letters 94, p. 095901 (2005). pdf-file

[58] ``Hamiltonian long wave expansions for water waves  over a rough bottom'',
(with P. Guyenne, D. Nicholls and C. Sulem), Proc. Royal Society A 461, (2005), pp. 1 - 35. pdf-file

The following is my book on Hamiltonian PDEs

[39] ``Problèmes de petits diviseurs dans les équations aux dérivées partielles'',
Panaromas et Synthèses
9, Société Mathématiques de France (2000).

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Last edited January 1 2018