Angular Regularity and Strichartz Estimates for the Wave Equation

By Jacob Sterbenz, Igor Rodnianski. 2004

171 citations recorded by the source corpus.

We prove here essentially sharp linear and bilinear Strichartz type estimates for the wave equations on Minkowski space, where we assume the initial data possesses additional regularity with respect to fractional powers of the usual angular momentum operators. In this setting, the range of (q,r) exponents vastly improves over what is available for the wave equations based on translation invariant derivatives of the initial data and the dispersive inequality. Two proofs of this result are given.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/68ed89e48fd981e4991a47e614dd8bcdc8a8b556

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In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Some remarks on Strichartz estimates for homogeneous wave equation (2005, background): “ [LdSo95] and [CaWe90]. Recently, there are many diverse advances in extending Strichartztype estimates for both wave equations and Schr¨odinger equations, such as in [Tao00], [Fc03p], [MaNaNaOz03p], [Stbz04p] etc. Since the appearance of [KeTa98], it is generally believed that the Strichartz estima”
Decay estimates for variable coefficient wave equations in exterior domains (2008, unknown): “, [16], [24], [9], [20], [7], and [23].”
Strichartz Estimates on Schwarzschild Black Hole Backgrounds (2008, unknown): “See for instance [20], [22], [40], [41], [42].”
Strichartz Estimates in Spherical Coordinates (2012, methodology): “In fact, for the wave equation (ω(ρ) = ρ) Strebenz [30] obtained almost optimal range of q, r and almost sharp required regularity (see also Section 4.”
Almost sure scattering for the 4D energy-critical defocusing nonlinear wave equation with radial data (2017, background): “4 (Radial Strichartz estimates; [41], [17]).”
Price's Law on Nonstationary Space-Times (2011, unknown): “applications; without being exhaustive we mention [59], [36], [56], [34], [35], [9], [46], [47], [58], [31].”