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

Nicolas Burq; Patrick Gérard; Nikolay Tzvetkov

Displaying similar documents to “The Schrödinger equation on a compact manifold : Strichartz estimates and applications”

Strichartz Estimates for the Schrödinger Equation with small Magnetic Potential

Vladimir Georgiev, Atanas Stefanov, Mirko Tarulli (2005)

Journées Équations aux dérivées partielles

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Existence globale et diffusion pour l’équation de Schrödinger non linéaire répulsive cubique sur $m a t h b b R^{3}$ en dessous l’espace d’énergie

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao (2002)

Journées équations aux dérivées partielles

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We sketch a proof of global existence and scattering for the defocusing cubic nonlinear Schrödinger equation in $H^{s} (ℝ^{3})$ for $s > \frac{4}{5}$ . The proof uses a new estimate of Morawetz type.

Global well-posedness and scattering for the mass-critical NLS

Benjamin Dodson (2011)

Journées Équations aux dérivées partielles

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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....

Global well-posedness for Schrödinger equations with derivative in a nonlinear term and data in low-order Sobolev spaces.

Takaoka, Hideo (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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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 $M = ℝ^{2} \times 𝕋^{2}$ and $M = ℝ^{3} \times 𝕋$ . The main ingredients are bi-linear and tri-linear refinements of Strichartz estimates which obey the critical scaling,...

Derivation of the Zakharov equations

Benjamin Texier (2005)

Journées Équations aux dérivées partielles

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Displaying similar documents to “The Schrödinger equation on a compact manifold : Strichartz estimates and applications”

Strichartz Estimates for the Schrödinger Equation with small Magnetic Potential

Existence globale et diffusion pour l’équation de Schrödinger non linéaire répulsive cubique sur m a t h b b R 3 en dessous l’espace d’énergie

Global well-posedness and scattering for the mass-critical NLS

Changing blow-up time in nonlinear Schrödinger equations

Global well-posedness for Schrödinger equations with derivative in a nonlinear term and data in low-order Sobolev spaces.

Energy Critical nonlinear Schrödinger equations in the presence of periodic geodesics

Derivation of the Zakharov equations

Existence globale et diffusion pour l’équation de Schrödinger non linéaire répulsive cubique sur $m a t h b b R^{3}$ en dessous l’espace d’énergie