Strichartz estimates for operators with nonsmooth coefficients and the nonlinear wave equation

By D. Tataru. 2000

167 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f1f77f9ad15c57ef7ee8334d6993a14c4df3e0d4

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

STRICHARTZ ESTIMATES FOR A SCHRÖDINGER OPERATOR WITH NONSMOOTH COEFFICIENTS (2002, background): “[18] one can relax the C(2) assumption on the coefficients to @(2)xa , @ta jk 2 L1xj ðL 1 t, xj Þ, j 1⁄4 1, .”
Global parametrices and dispersive estimates for variable coefficient wave equations (2007, methodology): “An alternative parametrix construction, based on the FBI transform, was later obtained in [32], [33] [35].”
Concerning the wave equation on asymptotically Euclidean manifolds (2008, unknown): “Kapitanski [13], Mockenhaupt-Seeger-Sogge [25], Smith [29], Bahouri-Chemin [1] [2], Tataru [34] [35] [37].”
Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients, II (2001, methodology): “Finally, due to Theorem 4 in [12], the endpoint estimate (corresponding to p = 2) follows from the nonendpoint estimate and the bound for the kernel K of Z, jK(y, ỹ)j (1 + jy ỹj) n 1 2”
On the Lp norm of spectral clusters for compact manifolds with boundary (2006, methodology): “The precise form here is a simple modification of the FBI transform used by Tataru in [18] and [19] to establish Strichartz estimates for low regularity metrics; the difference is that in our applications we use a Schwartz function with compactly supported Fourier transform, instead of the Gaussian,”
Strichartz estimates and local smoothing estimates for asymptotically flat Schr (2007, methodology): “This construction uses the FBI transform, an approach that is reminiscent of the earlier works [24, 25, 26] for the wave equation.”
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 Schr¨ odinger waves, following earlier work of Smith [20] and the author [ 22 ], [23] on the similar problem for the wave equation.,Instead, we take advantage of the simpler approach introduced by the auth”
Strichartz Estimates on Schwarzschild Black Hole Backgrounds (2008, methodology): “For smooth coe cients, this was rst shown in [32] and later for C(2) coe cients by [39] and [45, 46, 47].”
Decay estimates for variable coefficient wave equations in exterior domains (2008, methodology): “Using instead an approach based on the FBI transform, these estimates were extended to all dimensions in [26, 27, 28].”
ON THE FEFFERMAN–PHONG INEQUALITY AND RELATED PROBLEMS (2002, methodology): “[15]; however, we have chosen to redo it here.”
Sharp local well-posedness results for the nonlinear wave equation (2005, methodology): “The first result on Strichartz estimates leading to an improvement in the well-posedness problem for the nonlinear wave equation was obtained in Tataru [21]; roughly it says that if dg ∈ L 2 t L ∞ x , then the Strichartz estimates hold with a 1/4 derivative loss.”
Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds (2004, result): “After discussions with Daniel Tataru, we realized that the result of Theorem 1 can be deduced from Theorem 4 in [31].”
BILINEAR ESTIMATES AND APPLICATIONS TO NONLINEAR WAVE EQUATIONS (2001, methodology): “We refer the interested reader to the works of Chemin-Bahouri [6, 7], Tataru [ 49 , 50] and Klainerman [21].”