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Inventiones mathematicae, ISSN 0020-9910, 9/2008, Volume 173, Issue 3, pp. 449 - 475
...Invent. math. 173, 449–475 (2008) DOI: 10.1007/s00222-008-0124-z Random data Cauchy theory for supercritical wave equations I: local theory Nicolas Burq 1 , 2... 
Mathematics, general | Mathematics | MATHEMATICS | INVARIANT-MEASURES | GLOBAL EXISTENCE | NONLINEAR SCHRODINGER-EQUATION | Mathematics - Analysis of PDEs
Journal Article
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 9/2008, Volume 173, Issue 3, pp. 477 - 496
... Nicolas Burq 1 , 2 , Nikolay Tzvetkov 3 1 Département de Mathématiques, Université Paris XI, 91 405 Orsay Cedex, France 2 (e-mail: nicolas.burq@math.u-psud.fr ) 3... 
Mathematics, general | Mathematics | MATHEMATICS | NONLINEAR SCHRODINGER-EQUATION | INVARIANT-MEASURES | Studies | Mathematics - Analysis of PDEs | Analysis of PDEs
Journal Article
American journal of mathematics, ISSN 1080-6377, 2004, Volume 126, Issue 3, pp. 569 - 605
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 2015, Volume 336, Issue 1, pp. 101 - 130
We consider the damped wave equation on a manifold with imperfect geometric control. We show the sub-exponential energy decay estimate in (Christianson, J... 
ENERGY DECAY | PHYSICS, MATHEMATICAL
Journal Article
Journal of the European Mathematical Society, ISSN 1435-9855, 2014, Volume 16, Issue 1, pp. 1 - 30
The purpose of this article is to introduce for dispersive partial differential equations with random initial data, the notion of well-posedness (in the... 
EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | STRICHARTZ INEQUALITIES | INVARIANT-MEASURES | REGULARITY | DATA CAUCHY-THEORY | NONLINEAR SCHRODINGER-EQUATION
Journal Article
Developmental Biology, ISSN 0012-1606, 02/2014, Volume 386, Issue 2, pp. 461 - 472
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2016, Volume 18, Issue 6, p. 1650012
We study the decay of the semigroup generated by the damped wave equation in an unbounded domain. We first prove under the natural geometric control condition... 
uniform stabilization | exponential decay | control theory | unbounded domains | Klein-Gordon equation | Damped wave equation | variable damping | Carleman estimates | MATHEMATICS, APPLIED | STABILIZATION | MATHEMATICS | EXACT CONTROLLABILITY | ENERGY DECAY | Analysis of PDEs | Mathematics
Journal Article
Analysis and PDE, ISSN 2157-5045, 2013, Volume 6, Issue 6, pp. 1421 - 1427
The purpose of this note is to investigate the high-frequency behavior of solutions to linear Schrodinger equations. More precisely, Bourgain (1997) and... 
MATHEMATICS | MATHEMATICS, APPLIED | Schrodinger equations | defect-measures
Journal Article
1997, Astérisque, Volume 242., 122
Book
Annales Scientifiques de l'Ecole Normale Superieure, ISSN 0012-9593, 11/2017, Volume 50, Issue 6, pp. 1447 - 1498
For general nonlinear Klein-Gordon equations with dissipation we show that any finite energy radial solution either blows up in finite time or asymptotically... 
EXISTENCE | MATHEMATICS | WAVES | STATE SOLUTIONS | CONVERGENCE | INVARIANT FOLIATIONS | UNIQUENESS
Journal Article
1993, ISBN 9782856290231, Volume t. 121, fasc. 4., 128
Book
Journal of the American Mathematical Society, ISSN 0894-0347, 4/2004, Volume 17, Issue 2, pp. 443 - 471
Journal Article
Journal of the American Mathematical Society, ISSN 0894-0347, 09/2008, Volume 21, Issue 3, pp. 831 - 831
We prove that the defocusing quintic wave equation, with Dirichlet boundary conditions, is globally well posed on $H^1_0(\Omega) \times L^2(\Omega)$ for any... 
Mathematical manifolds | Spacetime | Wave equations | Integration by parts | Boundary conditions | Nonlinearity | Mathematical inequalities | Spherical coordinates | Wave equation | Dirichlet boundary conditions | MATHEMATICS | NORM | COMPACT MANIFOLDS | EQUATION | wave equation | Analysis of PDEs | Mathematics
Journal Article
Annales Scientifiques de l'Ecole Normale Superieure, ISSN 0012-9593, 2013, Volume 46, Issue 6, pp. 917 - 962
Journal Article
Memoirs of the American Mathematical Society, ISSN 1947-6221, 2018, Volume 256, Issue 1229
This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general... 
Paradifferential calculus | Water waves | Strichartz estimates | EXISTENCE | paradifferential calculus | FREE-BOUNDARY | WELL-POSEDNESS | FREE-SURFACE | MATHEMATICS | SOBOLEV SPACES | MOTION | NONSMOOTH COEFFICIENTS | REGULARITY | OPERATORS | GLOBAL-SOLUTIONS
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2012, Volume 44, Issue 5, pp. 3481 - 3501
...SIAM J. MATH. ANAL. c Vol. 44, No. 5, pp. 34813501 WEIGHTED EIGENFUNCTION ESTIMATES WITH APPLICATIONS TO COMPRESSED SENSING NICOLAS BURQ, SEMYON DYATLOV... 
Surfaces of revolution | Eigenfunctions | Compressed sensing | eigenfunctions | MATHEMATICS, APPLIED | compressed sensing | UNCERTAINTY PRINCIPLES | RECONSTRUCTION | FOURIER | surfaces of revolution
Journal Article
SIAM journal on control and optimization, ISSN 0363-0129, 01/2020, Volume 58, Issue 4, pp. 1893 - 1905
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2002, Volume 2002, Issue 5, pp. 221 - 241
The purpose of this note is to present a very natural and simple method to prove (for nontrapping geometries) the existence of resonance-free regions and to... 
MATHEMATICS | NUMBER | SCATTERING POLES | DECAY | RESONANCE | SINGULARITIES | EXACT CONTROLLABILITY | EXTERIOR PROBLEM | SHARP BOUNDS | WAVE-EQUATION | REFRACTION
Journal Article
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