Publications et prépublications de Thomas Duyckaerts

Prépublications/Preprints

• Global solutions with asymptotic self-similar behaviour for the cubic wave equation, avec Giuseppe Negro. Prépublication/Preprint 2023.

Articles acceptés/To appear

• On classification of non-radiative solutions for various energy-critical wave equations. Avec Charles Collot, Carlos Kenig et Frank Merle. Prépublication/Preprint 2022. À paraître à/To appear in Advances in Mathematics.
• On channels of energy for the radial linearised energy critical wave equation in the degenerate case. Avec Charles Collot, Carlos Kenig et Frank Merle. Prépublication/Preprint 2022. À paraître à/To appear in IMRN.
• Soliton resolution for the radial quadratic wave equation in six space dimensions. Avec Charles Collot, Carlos Kenig et Frank Merle. Prépublication/Preprint 2022. À paraître à/To appear in Vietnam Journal of Mathematics.

Articles publiés/Published articles

Depuis/Since 2020

• Soliton resolution for the critical wave equation with radial data in odd space dimensions, avec Carlos Kenig et Frank Merle. Acta Mathematica 230, No. 1, 1-92 (2023).
• Scattering for critical radial Neumann waves outside a ball, avec David Lafontaine. Revista Matematica Iberoamericana 38, No. 2, 659-703 (2022).
• Soliton resolution for critical co-rotational wave maps and radial cubic wave equation, avec Carlos Kenig,Frank Merle et Yvan Martel. Communication in Mathematical Physics 391, No. 2, 779-871 (2022).
• Threshold solutions in the focusing 3D cubic NLS equation outside a strictly convex obstacle. Avec Oussama Landoulsi et Svetlana Roudenko. Journal of functional analysis 282, No. 5, Article ID 109326, 55 p. (2022).
• A geometric condition for the uniform stability of linear magnetoelasticity, ESAIM COCV.27, Paper No. 82, 41 p. (2021).
• Scattering to a stationary solution for the superquintic radial wave equation outside an obstacle, avec Jianwei Urbain Yang. Annales de l'Institut Fourier (Grenoble),71, No. 5, 1845-1884 (2021).
• Self-similar solutions of energy-supercritical focusing wave equations in all dimensions, avec Wei Dai. Journal of Evolution Equation 21, No. 4, 4703-4750 (2021).
• Uniform a priori estimates for positive solutions of higher order Lane-Emden equations in Rn, avec Wei Dai. Publicacions Matemàtiques, Barcelona 65, No. 1, 319-333 (2021).
• On integrals over a convex set of the Wigner distribution, avec Bérangére Delourme et Nicolas Lerner. Journal of Fourier Analysis and Applications, 26 (2020) no. 1, 1-40.
• Exterior energy bounds for the critical wave equation close to the ground state, avec Carlos Kenig et Frank Merle. Communications in Mathematical Physics, 379, No. 3, 1113-1175 (2020).
• Decay estimates for nonradiative solutions of the energy-critical focusing wave equation, avec Carlos Kenig et Frank Merle (2019). À paraître à/To appear in Journal of Geometric Analysis, No. 7, 7036-7074 (2021).
• Excited resonance widths for Helmholtz resonators with straight neck, avec Alain Grigis et André Martinez. Journal of Spectral Theory 10 (2020) no.2, 561-580.

2015-2019

• Scattering profile for global solutions of the energy-critical wave equation, avec Carlos Kenig et Frank Merle Journal of the European Mathematical Society (JEMS), 21 (2019) no. 7, 2117-2162.
• Blow-up of a critical Sobolev norm for energy-subcritical and energy-supercritical wave equations, avec Jianwei Urbain Yang. Analysis & PDE, 11 (2018) no. 4, 983-1028.
• Universality of blow up profile for small blow up solutions to the energy critical wave map equation. International Mathematical Research Notices IMRN, 22 (2018), 6961-7025, avec Hao Jia, Carlos Kenig et Frank Merle.
• Blow-up of the critical Sobolev norm for nonscattering radial solutions of supercritical wave equations on R3, avec Tristan Roy. Bulletin de la Société Mathématique de France, 145 (2017) no. 3, 503-573.
• Soliton resolution along a sequence of times for the focusing energy critical wave equation, avec Hao Jia, Carlos Kenig et Frank Merle. Geometric and Functional Analysis, 27 (2017) no. 4. 798--862.
• Concentration-compactness and universal profiles for the non-radial energy critical wave equation, avec Carlos Kenig et Frank Merle Nonlinear Analysis 138 (2016), 44-82.
• Global existence for solutions of the focusing wave equation with the compactness property, avec Carlos Kenig et Frank Merle Annales de l'Institut Henri Poincaré, Analyse Non-Linéaire. 33 (2016) no. 6, 1675-1690.
• Solutions of the focusing nonradial critical wave equation with the compactness property, avec Carlos Kenig et Frank Merle. Annali della Scuola Normale Superiore di Pisa Classe di Scienze 15 (2016) 731-808.
• Resonance widths for general Helmholtz Resonators with straight neck, avec Alain Grigis et André Martinez. Duke Mathematical Journal (2016) 165, no. 14, 2793-2810.
• Local feedback stabilisation to a non-stationary solution for a damped non-linear wave equation, avec Kaïs Ammari et Armen Shirikyan. Mathematical Control & Related Fields 6 (2016), no. 1, 1--25.
• Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations, avec Carlos Kenig et Frank Merle. Communication in Pure and Applied Analysis 14 (2015), no. 4, 1275-1326.
• Global existence, scattering and blow-up for the focusing NLS on the hyperbolic space, avec Valeria Banica. Dyn. Partial Differ. Equ. 12 (2015), no. 1, 53-96.
• Going beyond the threshold: scattering and blow-up in the focusing NLS equation. Avec Svetlana Roudenko. Comm. Math. Phys. 334 (2015), no. 3, 1573-1615.

2010-2014

• Scattering for radial, bounded solutions of focusing supercritical wave equations, avec Carlos Kenig et Frank Merle. International Mathematical Research Notices IMRN. (2014) Vol. 2014 224-258.
• Classification of radial solutions of the focusing, energy-critical wave equation, avec Carlos Kenig et Frank Merle. Cambridge Journal of Mathematics 1 (2013), no. 1, 75-144.
• Profiles of bounded radial solutions of the focusing, energy-critical wave equation, avec Carlos Kenig et Frank Merle. Geometric and Functional Analysis. 22 (2012), no. 3, 639-698.
• Universality of the blow-up profile for small type II blow-up solutions of energy-critical wave equation: the non-radial case, avec Carlos Kenig et Frank Merle. J. Eur. Math. Soc. 14 (2012), no. 5, 1389-1454.
• Resolvent conditions for the control of parabolic equations. Avec Luc Miller. Journal of Functional Analysis 263 (2012), no. 11, 3641-3673.
• Universality of blow-up profile for small radial type II blow-up solutions of energy-critical wave equation, avec Carlos Kenig et Frank Merle. Journal of the European Mathematical Society 13 (2011), no. 3, 533-599.
• Maximizers for the Strichartz norm for small solutions of mass-critical NLS, avec Frank Merle et Svetlana Roudenko. Annali della Scuola Normale Superiore di Pisa Classe di Scienze. (5) 10 (2011), no. 2, 427-476.
• Minimal blow-up solutions to the mass-critical inhomogeneous NLS equation, avec Valeria Banica et Rémi Carles. Comm. Partial Differential Equations 36 (2011), no. 3, 487-531.
• Threshold solutions for the focusing 3D cubic Schrödinger equation, avec Svetlana Roudenko. Revista Matemática Iberoamericana 26 (2010), no. 1, 1-56.

2005-2009

• Dynamic of threshold solutions for energy-critical NLS, avec Frank Merle. Geometric and Functional Analysis 18 (2009), no. 6, 1787-1840.
• On scattering for NLS: from Euclidean to hyperbolic space. avec Valeria Banica et Rémi Carles. Discrete Continuous Dynamical Systems, series A 24 (2009), no. 4, 1113-1127.
• Scattering norm estimate near the threshold for energy-critical focusing semilinear wave equation, avec Frank Merle. Indiana University Mathematical Journal 58 (2009), no. 4, 1971-2001.
• Degenerated codimension 1 crossings and resolvent estimates, avec Clotilde Fermanian Kammerer et Thierry Jecko. Asymptotic Analysis 65 (2009), no. 3-4, 147-174.
• Scattering for the non-radial 3D cubic nonlinear Schroedinger equation, avec Justin Holmer et Svetlana Roudenko. Mathematical Research Letters 15 (2008), no. 6, 1233-1250.
• Dynamic of threshold solutions for energy-critical wave equation, avec Frank Merle. International Mathematical Research Paper IMRP 2008, Art ID rpn002, 67 pp.
• Non-uniform stability for bounded semi-groups on Banach spaces, avec Charles Batty. Journal of Evolution Equations 8 (2008), no. 4, 765-780.
• On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials, avec Xu Zhang et Enrique Zuazua. Annales de l'Institut Henri Poincaré Analyse Non Linéaire 25 (2008), no. 1, 1-41.
• Weighted Strichartz estimates for radial Schrödinger equation on noncompact manifolds, avec Valeria Banica. Dynamics of Partial Differential Equations 4 (2007), no. 4, 335-359.
• A singular critical potential for the Schrödinger operator. Canadian Mathematical Bulletin 50 (2007), no. 1, 35-47.
• Optimal decay rates of the energy of a hyperbolic-parabolic system coupled by an interface. Asymptot. Anal. 51 (2007) no. 1, 17-45. Inégalités de résolvante pour l'opérateur de Schrödinger avec potentiel multipolaire critique. Bull. Soc. Math. France 134 (2006), no. 2, 201-239.