Nicolas Burq

most citedMultilinear Eigenfunction Estimates And Global Existence For The Three Dimensional Nonlinear SchrÖdinger Equations

7 citations · 18 across the 5 of their papers we have counts for

collaborators

5 papers

math.AP2005★ 4 cited

On well-posedness for the Benjamin-Ono equation

N. Burq, F. Planchon

We prove existence of solutions for the Benjamin-Ono equation with data in $H^{s} (R)$ , $s > 0$ . Thanks to conservation laws, this yields global solutions for $H^{\frac{1}{2}} (R)$ data, w…

math.AP2005★ 1 cited

Spreading of quasimodes in the Bunimovich stadium

Nicolas Burq, Andrew Hassell, Jared Wunsch

We consider Dirichlet eigenfunctions $u_{λ}$ of the Bunimovich stadium $S$ , satisfying $(Δ - λ^{2}) u_{λ} = 0$ . Write $S = R \cup W$ where $R$ is the central rectangle and $W$ denotes the…

math.SP2005

Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds

N. Burq, P. Gerard, N. Tzvetkov

We give estimates for the $L^{p}$ norm ( $2 \leq p \leq + \infty$ ) of the restriction to a curve of the eigenfunctions of the Laplace Beltrami operator on a Riemannian surface. If the c…

math.AP2004★ 6 cited

Smoothing And Dispersive Estimates For 1d Schrödinger Equations With BV Coefficients And Applications

N. Burq, F. Planchon

We prove smoothing estimates for Schrödinger equations $i \partial_{t} ϕ + \partial_{x} (a (x) \partial_{x} ϕ) = 0$ with $a (x) \in BV$ , the space of functions with bounded total varia…

math.AP2004★ 7 cited

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 $M$ . We prove global existence of strong $H^{1}$ solutions on $M = S^{3}$ and $M = S^{2} \times S^{1}$ …