Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential

By Nicolas Burq, F. Planchon, John G. Stalker, A. Tahvildar-Zadeh. 2002

303 citations recorded by the source corpus.

Abstract We prove spacetime weighted- L 2 estimates for the Schrodinger and wave equation with an inverse-square potential. We then deduce Strichartz estimates for these equations.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/29eadcdab30dc5b1c1e25542f2d9dfd522007059

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Sobolev spaces adapted to the Schrödinger operator with inverse-square potential (2015, methodology): “This argument appears as Proposition 1 in [3] and relies on bounds of imaginary powers of La.”
Gaussian heat kernel upper bounds via the Phragmén–Lindelöf theorem (2006, unknown): “Such operators are called Schrödinger operators with the inverse-square potential and they are of substantial interest in analysis (see for example [13, 55] and references therein).”
Strichartz estimates and maximal operators for the wave equation in R3 (2012, methodology): “wave operators does not address the issue of reversed spacetime norms. Strichartz estimates for the wave equation in Rd with critical potentials were obtained by Burq–Planchon–Stalker–Tahvildar-Zadeh [BPST], [BPST2] and by D’Ancona–Pierfelice [DaPi]. The former results apply to potentials an with in”
Strichartz and Smoothing Estimates for Dispersive Equations with Magnetic Potentials (2007, methodology): “The method we shall follow is inspired by Burq et al. (2003) and Rodnianski and Schlag (2004) and consists in mixing Strichartz and smoothing estimates for the free operator with smoothing estimates for the perturbed operator.”
Strichartz estimates for the Wave and Schrodinger Equations with Potentials of Critical Decay (2004, background): “In [1] we showed that in the case where V (x) = a |x|2 the solution to the above equations satisfies generalized spacetime Strichartz estimates as long as a > −(n− 2)2/4.”
Restriction estimates, sharp spectral multipliers and endpoint estimates for Bochner-Riesz means (2012, background): “It is proved in [10] that the solution u(t) = e−itL f of the corresponding Schrödinger equation i∂tu + Lu = 0, u(0) = f satisfies Strichartz estimates (6.”
Counterexamples of Strichartz Inequalities for Schrodinger Equations with Repulsive Potentials (2006, background): “There is a huge literature on the subject, let us recall in particular [1], [2], [3], [6], [7], [8], [11], [16], [17], [18], [19], [21], even if the list is very far from being complete.”