Displaying similar documents to “Electromagnetic Schrödinger flow: multiplier methods for dispersion”

The Schrödinger equation on a compact manifold : Strichartz estimates and applications

Nicolas Burq, Patrick Gérard, Nikolay Tzvetkov (2001)

Journées équations aux dérivées partielles

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We prove Strichartz estimates with fractional loss of derivatives for the Schrödinger equation on any riemannian compact manifold. As a consequence we infer global existence results for the Cauchy problem of nonlinear Schrödinger equations on surfaces in the case of defocusing polynomial nonlinearities, and on three-manifolds in the case of quadratic nonlinearities. We also discuss the optimality of these Strichartz estimates on spheres.

Changing blow-up time in nonlinear Schrödinger equations

Rémi Carles (2003)

Journées équations aux dérivées partielles

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Solutions to nonlinear Schrödinger equations may blow up in finite time. We study the influence of the introduction of a potential on this phenomenon. For a linear potential (Stark effect), the blow-up time remains unchanged, but the location of the collapse is altered. The main part of our study concerns isotropic quadratic potentials. We show that the usual (confining) harmonic potential may anticipate the blow-up time, and always does when the power of the nonlinearity is L 2 -critical....

Energy Critical nonlinear Schrödinger equations in the presence of periodic geodesics

Sebastian Herr (2010)

Journées Équations aux dérivées partielles

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This is a report on recent progress concerning the global well-posedness problem for energy-critical nonlinear Schrödinger equations posed on specific Riemannian manifolds M with small initial data in H 1 ( M ) . The results include small data GWP for the quintic NLS in the case of the 3 d flat rational torus M = 𝕋 3 and small data GWP for the corresponding cubic NLS in the cases M = ℝ 2 × 𝕋 2 and M = ℝ 3 × 𝕋 . The main ingredients are bi-linear and tri-linear refinements of Strichartz estimates which obey the critical scaling,...