TY - JOUR
T1 - Semilinear schrödinger flows on hyperbolic spaces
T2 - Scattering in H1
AU - Ionescu, Alexandru D.
AU - Staffilani, Gigliola
N1 - Funding Information:
A. D. Ionescu was supported in part by a Packard Fellowship. G. Staffilani was supported in part by NSF Grant DMS 0602678
PY - 2009/7
Y1 - 2009/7
N2 - We prove global well-posedness and scattering in H1 for the defocusing nonlinear Schrödinger equations on the hyperbolic spaces ℍd, d ≥ 2, for exponents. The main unexpected conclusion is scattering to linear solutions in the case of small exponents σ; for comparison, on Euclidean spaces scattering in H1 is not known for any exponent and is known to fail for. Our main ingredients are certain noneuclidean global in time Strichartz estimates and noneuclidean Morawetz inequalities.
AB - We prove global well-posedness and scattering in H1 for the defocusing nonlinear Schrödinger equations on the hyperbolic spaces ℍd, d ≥ 2, for exponents. The main unexpected conclusion is scattering to linear solutions in the case of small exponents σ; for comparison, on Euclidean spaces scattering in H1 is not known for any exponent and is known to fail for. Our main ingredients are certain noneuclidean global in time Strichartz estimates and noneuclidean Morawetz inequalities.
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U2 - 10.1007/s00208-009-0344-6
DO - 10.1007/s00208-009-0344-6
M3 - Article
AN - SCOPUS:70350627598
SN - 0025-5831
VL - 345
SP - 133
EP - 158
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1
ER -