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

Nicolas Burq; Patrick Gérard; Nikolay Tzvetkov

Journées équations aux dérivées partielles (2001)

  • page 1-18
  • ISSN: 0752-0360

Abstract

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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.

How to cite

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Burq, Nicolas, Gérard, Patrick, and Tzvetkov, Nikolay. "The Schrödinger equation on a compact manifold : Strichartz estimates and applications." Journées équations aux dérivées partielles (2001): 1-18. <http://eudml.org/doc/93416>.

@article{Burq2001,
abstract = {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.},
author = {Burq, Nicolas, Gérard, Patrick, Tzvetkov, Nikolay},
journal = {Journées équations aux dérivées partielles},
keywords = {global existence results; optimality},
language = {eng},
pages = {1-18},
publisher = {Université de Nantes},
title = {The Schrödinger equation on a compact manifold : Strichartz estimates and applications},
url = {http://eudml.org/doc/93416},
year = {2001},
}

TY - JOUR
AU - Burq, Nicolas
AU - Gérard, Patrick
AU - Tzvetkov, Nikolay
TI - The Schrödinger equation on a compact manifold : Strichartz estimates and applications
JO - Journées équations aux dérivées partielles
PY - 2001
PB - Université de Nantes
SP - 1
EP - 18
AB - 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.
LA - eng
KW - global existence results; optimality
UR - http://eudml.org/doc/93416
ER -

References

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