Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients, II

By D. Tataru. 2001

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Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a6952dac4c17926e3b20b9769391c506d39f8f8b

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In Applied Mathematics

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Citations in the corpus

Global parametrices and dispersive estimates for variable coefficient wave equations (2007, methodology): “transform, was later obtained in [29], [ 30 ] [32].”
Strichartz Estimates on Schwarzschild Black Hole Backgrounds (2008, background): “For smooth coe cients, this was rst shown in [32] and later for C(2) coe cients by [39] and [45, 46, 47].”
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.”
On the Lp norm of spectral clusters for compact manifolds with boundary (2006, methodology): “4), the term G̃ may have large L(1)L(2) norm if θ is small, in contrast to the setting of [19].”
Strichartz estimates for the wave equation on manifolds with boundary (2008, methodology): “Note that the restrictions on (p, q) in Theorem 1.1 are precisely that σ(p,q) 1/p. Estimate (2.2) is established through the parametrix construction from [21], together with the use of the V p2 spaces of Koch and Tataru [14].”
Global existence for energy critical waves in 3-d domains (2006, result): “MR1964470 (2003m:58016) [17] Daniel Tataru.”
ON THE FEFFERMAN–PHONG INEQUALITY AND RELATED PROBLEMS (2002, methodology): “[16] , where the first two terms are used to construct a parametrix for the wave equation with C 2 coefficients.”
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].”
Sharp local well-posedness results for the nonlinear wave equation (2005, background): “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 ESTIMATES FOR A SCHRÖDINGER OPERATOR WITH NONSMOOTH COEFFICIENTS (2002, methodology): “Wave operators with C(2) coefficients are considered in Smith([14]) in 2þ1 and 3þ1 dimensions and in Tataru([19]) in any dimension; this can be further relaxed to @(2)g 2 L1ðL1Þ, see Tataru.”
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].”
Decay estimates for variable coefficient wave equations in exterior domains (2008, background): “Strichartz estimates as stated above are lost (see [18], [22]) and only certain estimates with losses are available [ 28 , 29].”