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Address: Département de Mathématiques, Universite Paris-Saclay, Bat. 307, 91405 Orsay Cedex FRANCE Mail: nicolas.burq@universite-paris-saclay.fr Bureau: 3A11 (3rd floor)

ERC project GEOEDP

Some talks

• 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)
• Données initiales aléatoires et théorie de Cauchy pour les ondes sur-critiques, I.H.P. 30/11/2007 (.pdf)
• Low regularity water-waves: canal and swimming pools, Journées EDP Biarritz 2008 (.pdf)
• Random data for PDE's ICM 2010, Hyderabad (text)(slides)
• Control and stabilization of Schrödinger equations on tori: rough potentials Winter school Saint Etienne de Tinée jan 4th--8th 2013 (.pdf)
• The Gaussian free field, Gibbs measures and NLS on planar domains, LAGA Paris-Nord, feb. 20th, 2014(.pdf)
• Large time dynamics for the damped semi-linear Klein-Gordon equation, I.H.E.S. 30/06/2016 (.pdf)
• Control and stabilization of Schrödinger and wave linear equations on tori (HYP 2016, Aachen, aug. 2nd 2016) (.pdf)
• Control and stabilization from geodesic domains (Séminaire Paris-Nord) décembre 2017 (.pdf)
• Almost sure global existence and scattering for the one dimensional NLS (EPFL), octobre 2017 (.pdf )

• My articles:

My articles on scattering theory
 

• 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)

My articles on the control of wave and Schrödinger equations  

• 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
• N. Burq and M. Zworski Rough controls for Schroedinger operators on 2-tori arXiv:1712.08635
• N. Burq and P. Gérard Stabilisation of wave equations on the torus with rough dampings arxiv:1801.00983

My articles on non linear wave and Schrödinger equations

• "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

• "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
• N. Burq, D. dos Santos and K. Krupchyk From semiclassical Strichartz estimates to uniform $L^p$ resolvent estimates on compact manifolds.pdf

• 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 and G. Lebeau. Probabilistic Sobolev embeddings, applications to eigenfunctions estimates, Geometric and spectral analysis,Contemp. Math. 630, pp307--318, Amer. Math. Soc., Providence, RI (2014)..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

• 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

  
  

   

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