Nicolas Burq

Professeur

Departement de Mathématiques

English page

Adresse:

Département de Mathématiques,

Universite Paris-Sud,

Bat. 425, 91405 Orsay Cedex
FRANCE

Mail: nicolas.burq@u-psud.fr

Bureau: 236

Curriculum vitae

Quelques exposes

Non-linear Evolution Equations on Domains with Boundary (.pdf)
The Schrödinger equation on a compact manifold: Strichartz estimates and applications. Journées "Équations aux Dérivées Partielles" (Avec P. Gerard et N. Tzvetkov), Exp. No. V, 18 pp., Univ. Nantes, Nantes, 2001. (.pdf)
Inegalites de Sogge bilineaires et Equations de Schrodinger non lineaires, Seminaire EDP de l'Ecole Polytechnique (2002-03) (Avec P. Gerard et N. Tzvetkov) (.pdf)
Estimees multilineaires de projecteurs spectraux et Equations de Schrodinger non lineaires, Seminaire EDP de l'Ecole Polytechnique (2003-04) (Avec P. Gerard et N. Tzvetkov) (.pdf)
Control Theory and high energy eigenfunctions (2003-04) Journées "Équations aux Dérivées Partielles" (Avec M. Zworski), Univ. Nantes, Nantes, 2004 (.pdf)
Control and stabilization of Schrödinger equations on tori (HYP 2016, Aachen, aug. 2nd 2016) (.pdf)

Mes articles:

Mes articles sur la theorie du scattering

N. Burq: Pôles de diffusion engendrés par un coin. Astérisque, 242 (1997). (.dvi).(.ps).
N. Burq: Décroissance de l'énergie locale de l'équation des ondes pour le problème extérieur et absence de résonance au voisinage du réel. Acta Mathématica, 180, p 1-29, 1998. (.dvi).(.ps).
N. Burq: Formules de trace, Résonances et quasi-modes (d'après Sjostrand-Zworski, Stefanov-Vodev et al). Séminaire Bourbaki 1998-1999. 856. (.dvi).(.ps).
N. Burq and M. Zworski: Resonance expansions in semi-classical propagation Comm. Math. Phys. 223 (2001), no. 1, 1--12.(.dvi) (.ps)
N. Burq: Lower bounds for shape resonances widths of long range Schrodinger operators. Amer. J. Math. 124 (2002), no. 4, 677--735" (.dvi) (.ps)
N. Burq: Semi-classical estimates for the resolvent in non trapping geometries". Int. Math. Res. Not. 2002, no. 5, 221--241(.dvi) (.ps)
J-F. Bony, N. Burq, and T. Ramond. Minoration de la résolvante dans le cas captif. C. R. Math. Acad. Sci. Paris, 348(23-24):1279–1282, 2010. (.pdf)

Mes articles sur le contrôle des ondes et de Schrodinger

N. Burq: "Contrôle de l'équation des plaques en présence d'obstacles strictement convexes" Mémoire de la S.M.F. 55 (1993). (.dvi)(.ps)
N. Burq: "Un théorème de controle d'une structure multidimensionnelle" Communications in Partial Differential Equations, 19 (1-2) . p.199-211 (1994). (.dvi) (.ps)
N. Burq: "Contrôle de l'équation des ondes dans des ouverts peu réguliers." Asymptotic Analysis, 14, p.157-191, (1997). (.dvi).(.ps).
N. Burq, P. Gérard: Condition Nécessaire et suffisante pour la contrôlabilité exacte des ondes" Comptes Rendus de l'Académie des Sciences. t. 325, Série I, p.749-752 (1997). (.dvi).(.ps).
"Mesures semi-classiques et mesures de défaut" (d'après P.Gérard, L.Tartar et al.). Astérisque 245, p. 167-196, Séminaire Bourbaki 1996-1997. (.dvi).(.ps).
N. Burq: "Contrôle de l'équation des ondes dans des ouverts comportant des coins." Bull. de la Soc. Math. de France, 126, p. 601-637, 1998. (.dvi).(.ps).
N. Burq, G. Lebeau: Mesures de défaut, application au système de Lamé . Ann. Sci. École Norm. Sup. (4) 34 (2001), no. 6, 817--870.(.dvi ).(.ps)
N. Burq and M. Zworski. Geometric control in the presence of a black box. Jour. of the American Math. Society, 17(2):443–471, 2004.
N. Burq, P. Gérard: Controle optimal des equations aux derivees partielles. Cours de l'Ecole Polytechnique. 2002.
N. Burq and M. Hitrik. Energy decay for damped wave equations on partially rectangular domains. Math. Res. Lett., 14(1):35–47, 2007.
N. Burq and M. Zworski. Control for Schrödinger operators on tori. Math. Res. Lett., 19(2):309–324, 2012. .pdf
J. Bourgain, N. Burq, and M. Zworski. Control for Schrödinger operators on 2-tori: rough potentials. J. Eur. Math. Soc. (JEMS), 15(5):1597–1628, 2013. .pdf
N. Burq and C. Zuily. Laplace Eigenfunctions and Damped Wave Equation on Product Manifolds. Appl. Math. Res. Express. AMRX, 2:296–310, 2015. .pdf
N. Burq and C. Zuily. Concentration of Laplace eigenfunctions and stabilization of weakly damped wave equation. Comm. Math. Phys., 345(3):1055–1076, 2016..pdf
N. Burq and R. Joly. Exponential decay for the damped wave equation in unbounded domains. Commun. Contemp. Math., 18(6):1650012, 27, 2016. .pdf

Mes articles sur les ondes et Schrödinger non lineaires

"Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds" (avec P. G"erard et N. Tzvetkov) Amer. J. Math. 126 (2004), no. 3, 569--605 (.dvi)(.ps)
"An instability property of the nonlinear Schrodinger equation on Sd" (avec P. G"erard et N. Tzvetkov). Math. Res. Let. 9 (2002), no. 2-3, 323--335. (dvi)(.ps)
"Two singular dynamics of the nonlinear Schrodinger equation on a plane domain" (avec P. G"erard et N. Tzvetkov). Geom. Funct. Anal. 13 (2003), no. 1, 1--19 (.dvi)(.ps)
" The Cauchy problem for the non linear Schrodinger equation on a compact manifold" (avec P. Gerard et N. Tzvetkov) J. Nonlinear Math. Phys. 10 (2003), suppl. 1, 12--27 (.ps)(.pdf).
" An example of singular dynamics for the nonlinear Schrodinger equation on bounded domains (avec P. G"erard et N. Tzvetkov). Hyperbolic problems and related topics, 57--66, Grad. Ser. Anal., Int. Press, Somerville, MA, 2003 (.dvi) (.ps)
"Smoothing effect for Schr\"odinger boundary value problems". Duke Math. Jour 123-2 (2004), 403--427. (.pdf).
Global Strichartz Estimates for nontrapping Geometries: About an Article by H. Smith and C. Sogge. Communications in Partial Differential Equations 28 (2003), no. 9-10, 1675--1683 (article).
Strichartz estimates for the Wave and Schrodinger Equations with the Inverse-Square Potential (avec F. Planchon, J. G. Stalker, et A. Shadi Tahvildar-Zadeh). Jour. of Fun. Anal. 203 (2003), 2, 519--549 (article)
Strichartz estimates for the Wave and Schrodinger Equations with critical decay (avec F. Planchon, J. G. Stalker, et A. Shadi Tahvildar-Zadeh). Preprint (2003) (article)
On non-linear Schrodinger equations in exterior domains (with P. G"erard et N. Tzvetkov) . Ann. I.H.P. 21 (2004), no. 3, 295--318 21 (2004), no. 3, 295--318(.dvi)(.ps)
Bilinear Eigenfunction estimates and the Nonlinear Schrodinger equations on surfaces (with P. G"erard et N. Tzvetkov) . Invent. Math. 159 (2005), no. 1, 187--223 (.pdf)
"Multilinear estimates for the Laplace spectral projectors on compact manifolds" (with P. Gerard et N. Tzvetkov). C. R. Math. Acad. Sci. Paris 338 (2004), no. 5, 359--364 .(article)
"Multilinear Eigenfunction Estimates And Global Existence For The Three Dimensional Nonlinear Schrodinger Equations" (with P. Gerard et N. Tzvetkov). Ann. Sci. ƒcole Norm. Sup. (4) 38 (2005), no. 2, 255--301 (.pdf)
"Instability for the semiclassical non-linear Schr\"odinger equation" (avec M. Zworski). A paraitre a Comm. Math. Phys. 2003.
"Smoothing And Dispersive Estimates For 1d Schr\"odinger Equations With BV Coefficients And Applications" (avec F. Planchon To appear in Journal of Functional Analysis). Preprint 2004,
"On well-posedness for the Benjamin-Ono equation " (avec F. Planchon). Preprint 2005.
"Global existence for energy critical waves in 3-d domains (avec G. Lebeau et F. Planchon) Journal of the A.M.S., (21):831--845, 2008.
N. Burq and F. Planchon. Global existence for energy critical waves in 3-d domains: Neumann boundary conditions. American Journal of mathematics, 131(6):1715–1742, 2009. To appear in American Journal of Math. 2008
N.Burq, P.Gérard and N.Tzvetkov. High frequency solutions of the non linear Schrödinger equation on surfaces. Quart. Appl. Math., 68(1):61–71, 2010. .pdf
N. Burq. Large-time dynamics for the one-dimensional Schrödinger equation. Proc. Roy. Soc. Edin- burgh Sect. A, 141(2):227–251, 2011.
N.Burq, G. Raugel ,and W. Schlag. Long time dynamics for damped klein-gordon equations. Annales Scientifiques de l’Ecole Normale Supérieure, to appear, 2017, .pdf

Mes articles sur les comportement des fonctions propres du laplacien et les équations linéaires

"Eigenfunctions for partially rectangular billiards" (avec M. Zworski). Preprint 2003.
N. Burq. Global Strichartz estimates for nontrapping geometries: about an article by H. F. Smith and C. D. Sogge. Comm. Partial Differential Equations, 28(9-10):1675–1683, 2003. .pdf
N. Burq. Smoothing effect for Schrödinger boundary value problems. Duke Math. J., 123(2):403–427, 2004.pdf
N. Burq, P. Gérard, and N. Tzvetkov. Multilinear estimates for the Laplace spectral projector on compact manifolds. Comptes rendus de l’académie des sciences, 338(Sér. I):359–364, 2004..pdf
"Quantum ergodicity of boundary value problems: a control theory approach" Can. Bull. of Math. 48 (2005), no. 1, 3--15 2003
"Bouncing ball modes and quantum chaos" (avec M. Zworski). (article) SIAM Rev. 47 (2005), no. 1, 43--49.
N. Burq and M. Zworski. Bouncing ball modes and quantum chaos. S.I.A.M. Review, 47(1):43–49, 2005..pdf
N. Burq, P. Gérard, and N. Tzvetkov. Restrictions of the Laplace-Beltrami eigenfunctions to sub- manifolds. Duke Math. J., 138(3):445–486, 2007..pdf
N. Burq, A. Hassell, and J. Wunsch. Spreading of quasimodes in the Bunimovich stadium. Proc. Amer. Math. Soc., 135(4):1029–1037, 2007. A paraitre aux Proc. AMS. (2005)
N. Burq, C. Guillarmou, and A. Hassell. Strichartz estimates without loss on manifolds with hyper- bolic trapped geodesics. Geom. Funct. Anal., 20(3):627–656, 2010..pdf
N. Burq, S. Dyatlov, R. Ward, and M. Zworski. Weighted eigenfunction estimates with applications to compressed sensing. SIAM J. Math. Anal., 44(5):3481–3501, 2012..pdf
N. Burq. Semiclassical measures for inhomogeneous Schrödinger equations on tori. Anal. PDE, 6(6):1421–1427, 2013..pdf
N. Burq and H. Christianson. Imperfect geometric control and overdamping for the damped wave equation. Comm. Math. Phys., 336(1):101–130, 2015..pdf
T. Alazard, N. Burq, and C. Zuily. A stationary phase type estimate. Preprint http://arxiv.org/abs/1511.01439, to appear in Proceedings of the American Mathematical So- ciety, 2016.pdf

Mes articles sur les EDP à donnees initales aleatoires et plus généralement EDP et Probabilités

N. Burq and N. Tzvetkov. Invariant measure for a three dimensional nonlinear wave equation. International Mathematics Research Notices n. 22, 2007.pdf
N. Burq and N. Tzvetkov. Random data cauchy theory for supercritical wave equations I: Local theory. Inventiones Mathematicae, 173:449–475, 2008..pdf
N. Burq and N. Tzvetkov. Random data cauchy theory for supercritical wave equations II: A global result. Inventiones Mathematicae, 173:477–496, 2008. .pdf
N. Burq and G. Lebeau. Injections de Sobolev probabilistes et applications. Ann. Sci. Éc. Norm. Supér. (4), 46(6):917–962, 2013..pdf
N. Burq, L. Thomann, and T. Tzvetkov. Global infinite energy solutions for the cubic wave equation. Bulletin de la Société Mathématique de France, 143(2):301–313, 2015. .pdf
N. Burq and Nikolay Tzvetkov. Probabilistic well-posedness for the cubic wave equation. J. Eur. Math. Soc. (JEMS), 16(1):1–30, 2014.
Nicolas Burq, Laurent Thomann, and Nikolay Tzvetkov. Remarks on the Gibbs measures for nonlinear dispersive equations, to appear in Annales de la Faculté des Sciences de Toulouse..pdf

Mes articles sur le système des ondes de surface (Euler frontière libre, water waves)
T. Alazard, N. Burq, and C. Zuily. On the water-wave equation with surface tension. Duke Math Journal, 158(3):413–499, 2011..pdf
T. Alazard, N. Burq, and C. Zuily. Strichartz estimates for water waves. Annales Scientifiques de l’E.N.S., 44:855–903, 2011. .pdf
Thomas Alazard, N. Burq, and C. Zuily. The water-wave equations: from Zakharov to Euler. In Studies in phase space analysis with applications to PDEs, volume 84 of Progr. Nonlinear Differential Equations Appl., pages 1–20. Birkhäuser/Springer, New York, 2013.pdf
T. Alazard, N. Burq, and C. Zuily. On the Cauchy problem for gravity water waves. Invent. Math., 198(1):71–163, 2014..pdf
T. Alazard, N. Burq, and C. Zuily. Cauchy theory for the gravity water waves system with non-localized initial data. Annales de l’Institut Henri Poincare (C) Non Linear Analysis, 2015. doi:10.1016/j.anihpc.2014.10.004..pdf
T. Alazard, N. Burq, and C. Zuily. Strichartz estimates and the Cauchy problem for the gravity water waves equations. to appear in Memoirs of the AMS, pages 1–129, 2016. http://arxiv.org/abs/1404.4276..pdf