Counterexamples of Strichartz Inequalities for Schrodinger Equations with Repulsive Potentials
By M. Goldberg, Luis Vega, Nicola Visciglia. 2006
76 citations recorded by the source corpus.
MICHAEL GOLDBERG, LUIS VEGA, AND NICOLA VISCIGLIAAbstract. In each dimension n ≥ 2, we construct a class of nonnegativepotentials that are homogeneous of order −σ, chosen from the range 0 ≤ σ < 2,and for which the perturbed Schro¨dinger equation does not satisfy global intime Strichartz estimates.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0908bb34259480d6b57c5465bc21b1d62bcf5095
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In Applied Mathematics
- Jiqiang Zheng
- Piero D'Ancona
- Luca Fanelli
- Luis Vega
- Junyong Zhang
- Nicola Visciglia
- Michael Christ
- Herbert Koch
In Mathematical Physics
- Jiqiang Zheng
- Piero D'Ancona
- Luca Fanelli
- Luis Vega
- Junyong Zhang
- Nicola Visciglia
- Michael Christ
- Herbert Koch
Citations in the corpus
- Scattering theory for nonlinear Schrödinger equations with inverse-square potential (2013, background): “In the study of Strichartz estimates for the propagators e , the decay V (x) ∼ |x|−2 is borderline in order to guarantee validity of Strichartz estimate; see Goldberg-Vega-Visciglia [15].”
- Endpoint Strichartz estimates for the magnetic Schrodinger equation (2009, background): “It is now clear that in this case the decay V (x) ∼ 1/|x|2 is critical for the validity of Strichartz estimates; suitable counterexamples were constructed in [17].”