Name
Abstract | ||
|---|---|---|
We study the Schrodinger-Poisson system on the unit sphere S(2) of R(3), modeling the quantum transport of charged particles confined on a sphere by an external potential. Our first results concern the Cauchy problem for this system. We prove that this problem is regularly well-posed on every H(s)(S(2)) with s > 0, and not uniformly well-posed on L(2)(S(2)). The proof of well-posedness relies on multilinear Strichartz estimates, and the proof of ill-posedness relies on the construction of a counterexample which concentrates exponentially on a closed geodesic. In a second part of the paper, we prove that this model can be obtained as the limit of the three-dimensional Schrodinger-Poisson system, singularly perturbed by an external potential that confines the particles in the vicinity of the sphere. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1137/100813634 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | DocType | Volume |
Schrodinger-Poisson,confined quantum transport,asymptotic analysis,multilinear Strichartz estimates | Journal | 43 |
Issue | ISSN | Citations |
3 | 0036-1410 | 0 |
PageRank | References | Authors |
0.34 | 2 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Patrick Gérard | 1 | 0 | 0.34 |
| Florian Méhats | 2 | 80 | 14.01 |