STRICHARTZ ESTIMATES FOR A SCHRÖDINGER OPERATOR WITH NONSMOOTH COEFFICIENTS

By Gigliola Staffilani, D. Tataru. 2002

227 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e9dd8fa232486c5bf53f59ff5b326bde36383f46

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Citations in the corpus

Strichartz estimates and local smoothing estimates for asymptotically flat Schr (2007, background): “Local-in-time Strichartz estimates for variable coefficient operators have also been established in [23], [12], and [19] provided, amongst other things, that the coefficients are non-trapping.”
Dispersive estimates for principally normal pseudodifferential operators (2004, result): “Similar results were obtained for the Schrödinger equation in Staffilani-Tataru [19] (C(2) coefficients) and in Burq-Gerard-Tzvetkov [1] (smooth coefficients).”
Strichartz and Smoothing Estimates for Dispersive Equations with Magnetic Potentials (2007, background): “We must also mention the papers Robbiano and Zuily (2005), Staffilani and Tataru (2002), and Tataru and Geba (2005) containing some local estimates in the fully variable coefficient case.”
Strichartz estimates for long range perturbations (2005, background): “The proof of Theorem 2 is based on ideas introduced in [29, 6].”
Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds (2004, methodology): “After discussions with Daniel Tataru, we realized that the result of Theorem 1 can be deduced from Theorem 4 in [31].”
Time decay for solutions of Schrödinger equations with rough and time-dependent potentials (2001, background): “dispersive property fails, see Bourgain [Bo3] for the case of the torus, Staffilani, Tataru [ ST ] for variable coefficients, and Burq, Gerard, Tzvetkov [BGT] for the case of equations on Riemannian manifolds.”
Counterexamples of Strichartz Inequalities for Schrodinger Equations with Repulsive Potentials (2006, methodology): “At this respect it is important to mention [11] and [21] where the local smoothing estimate is used to conclude estimates as (1.”
Quintic NLS in the exterior of a strictly convex obstacle (2012, background): “Using this argument, Strichartz estimates have been proved for merely non-trapping obstacles; for further discussion see [6, 11, 38, 54, 64].”
Parametrices and dispersive estimates for Schrödinger operators with variable coefficients (2008, methodology): “The results in [21] are based on a phase space analysis of the spatially localized part of the Schrödinger waves, following earlier work of Smith [20] and the author [22], [23] on the similar problem for the wave equation.”
Global parametrices and dispersive estimates for variable coefficient wave equations (2007, background): “[29] Gigliola Staffilani and Daniel Tataru.”
Sharp Strichartz estimates on nontrapping asymptotically conic manifolds (2004, methodology): “The nonendpoint hypothesis q 6= 2 is exploited (as in [24], [1]) via the Christ-Kiselev lemma [7], which allows one to decouple the Strichartz and the local smoothing aspects of our estimates.”