Strichartz estimates for the Wave and Schrodinger Equations with Potentials of Critical Decay

By Nicolas Burq, F. Planchon, John G. Stalker, A. Tahvildar-Zadeh. 2004

215 citations recorded by the source corpus.

We prove weighted L^2 (Morawetz) estimates for the solutions of linear Schrodinger and wave equation with potentials that decay like |x|^{-2} for large x, by deducing them from estimates on the resolvent of the associated elliptic operator. We then deduce Strichartz estimates for these equations.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/148e4c63054a9ccc957db9e66c231232a7fad923

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Strichartz and Smoothing Estimates for Dispersive Equations with Magnetic Potentials (2007, methodology): “…estimate (2.40) and assumption (1.11), we conclude I1 LpḢ 1 q − 1p − 12 q f L2 Consider now the second term II , or more generally II1 = eit D ∫ D −1e−is D c x u ds Proceeding as in Burq et al. (2004), we shall use the following estimate from Ben-Artzi (1994) (see also Hoshiro, 1997)∥∥ x −1 D…”
Local decay of waves on asymptotically flat stationary space-times (2009, background): “There is by now an extensive literature devoted to this topic and its applications; without being exhaustive we mention Strauss [43], Keel-Smith-Sogge [23, 24], Burq-Planchon-Stalker-TahvildarZadeh [6], Metcalfe-Sogge [32, 33].”
Parametrices and dispersive estimates for Schrödinger operators with variable coefficients (2008, unknown): “We note that the bound (9) can be used to connect the present work with estimates proved for the flat Laplacian with inverse square potentials, see [4] and references therein.”
Sobolev spaces adapted to the Schrödinger operator with inverse-square potential (2015, methodology): “Several instances where this occurs in physics are discussed in the mathematical papers [3, 4, 17, 38, 39]; they range from combustion theory to the Dirac equation with Coulomb potential, and to the study of perturbations of classic space-time metrics such as Schwarzschild and Reissner–Nordström.”
Price's Law on Nonstationary Space-Times (2011, unknown): “We now record the commutators of P with vector fields.”