AIMS Laboratory, McMaster University
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.
DOI:10.1007/s00220-016-2781-x.
[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.
[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
[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
[39] ``Problèmes de petits diviseurs dans les
équations aux dérivées partielles'',
Panaromas et Synthèses 9,
Société Mathématiques de France (2000).