23 citations · 69 across the 8 of their papers we have counts for
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Multilinear Eigenfunction Estimates And Global Existence For The Three Dimensional Nonlinear SchrÖdinger Equations
N. Burq, P. Gerard, N. Tzvetkov
We study nonlinear Schrödinger equations, posed on a three dimensional Riemannian manifold . We prove global existence of strong solutions on and …
Multilinear eigenfunction estimates for the Laplace spectral projectors on compact manifolds
N. Burq, P. Gerard, N. Tzvetkov
The purpose of this note is to extend to any space dimension the bilinear estimate for eigenfunctions of the Laplace operator on a compact manifold (without boundary) obtained in a…
Bouncing ball modes and quantum chaos
N. Burq, M. Zworski
Quantum ergodicity of classically chaotic systems has been studied extensively both theoretically and experimentally, in mathematics, and in physics. Despite this long tradition we…
Control in the presence of a black box
N. Burq, M. Zworski
We apply the ``black box'' scattering theory to problems in control theory and in high energy eigenvalue scarring.
Quantum ergodicity of boundary values of eigenfunctions: A control theory approach
Nicolas Burq
Consider , a bounded domain in , which is a Riemanian manifold with piecewise smooth boundary and suppose that the billiard associated to the geodesic flow reflec…
Strichartz estimates for the Wave and Schrodinger Equations with the Inverse-Square Potential
Nicolas Burq, Fabrice Planchon, John G. Stalker +1
We prove spacetime weighted-L^2 estimates for the Schrodinger and wave equation with an inverse-square potential. We then deduce Strichartz estimates for these equations.