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pro vyhledávání: '"Burq, N."'
$H^1$ scattering for mass-subcritical NLS with short-range nonlinearity and initial data in $\Sigma$
We consider short-range mass-subcritical nonlinear Schr\"odinger equations and we show that the corresponding solutions with initial data in $\Sigma$ scatter in $H^1$. Hence we up-grade the classical scattering result proved by Yajima and Tsutsumifro
Externí odkaz:
http://arxiv.org/abs/2111.07802
Autor:
Burq, N., Ducomet, B.
Publikováno v:
Kyoto J. Math. 60, no. 3 (2020), 911-939
In this article, we study the decay of the solutions of Schr\"odinger equations in the exterior of an obstacle. The main situations we are interested in are the general case (no non-trapping assumptions) or some weakly trapping situations
Commen
Commen
Externí odkaz:
http://arxiv.org/abs/1802.04008
The purpose of this note is to prove a stationary phase estimate well adapted to parameter dependent phases. In particular, no discussion is made on the positions (and behaviour) of critical points, no lower or upper bound on the gradient of the phas
Externí odkaz:
http://arxiv.org/abs/1511.01439
For general nonlinear Klein-Gordon equations with dissipation we show that any finite energy radial solution either blows up in finite time or asymptotically approaches a stationary solution in $H^1\times L^2$. In particular, any global solution is b
Externí odkaz:
http://arxiv.org/abs/1505.05981
Autor:
Burq, N, Zuily, Claude
- The purpose of this article is to study possible concentrations of eigenfunc-tions of Laplace operators (or more generally quasi-modes) on product manifolds. We show that the approach of the first author and Zworski [10, 11] applies (modulo rescall
Externí odkaz:
http://arxiv.org/abs/1503.05513
Autor:
Burq, N., Zuily, Claude
- In this article, we prove some universal bounds on the speed of concentration on small (frequency-dependent) neighborhoods of submanifolds of L 2-norms of quasi modes for Laplace operators on compact manifolds. We deduce new results on the rate of
Externí odkaz:
http://arxiv.org/abs/1503.02058
Autor:
Burq, N., Planchon, F.
We prove that the defocusing quintic wave equation, with Neumann boundary conditions, is globally wellposed on $H^1_N(\Omega) \times L^2(\Omega)$ for any smooth (compact) domain $\Omega \subset \mathbb{R}^3$. The proof relies on one hand on $L^p$ est
Externí odkaz:
http://arxiv.org/abs/0711.0275
Autor:
Burq, N., Tzvetkov, N.
We study the local existence of strong solutions for the cubic nonlinear wave equation with data in $H^s(M)$, $s<1/2$, where $M$ is a three dimensional compact riemannian manifold. This problem is supercritical and can be shown to be strongly ill-pos
Externí odkaz:
http://arxiv.org/abs/0707.1447
Autor:
Burq, N., Tzvetkov, N.
We study the long time behavior of the subcritical (subcubic) defocussing nonlinear wave equation on the three dimensional ball, for random data of low regularity. We prove that for a large set of radial initial data in $\cap_{s<1/2} H^s(B(0,1))$ the
Externí odkaz:
http://arxiv.org/abs/0707.1445
Autor:
Burq, N., Tzvetkov, N.
We prove that the subquartic wave equation on the three dimensional ball $\Theta$, with Dirichlet boundary conditions admits global strong solutions for a large set of random supercritical initial data in $\cap_{s<1/2} H^s(\Theta)$. We obtain this re
Externí odkaz:
http://arxiv.org/abs/0707.1448