Details

Autor(en) / Beteiligte

• HASSELL, ANDREW
• TAO, TERENCE
• WUNSCH, JARED

Titel

A Strichartz Inequality for the Schrödinger Equation on Nontrapping Asymptotically Conic Manifolds

Ist Teil von

• Communications in partial differential equations, 2005-04, Vol.30 (1-2), p.157-205

Ort / Verlag

Taylor & Francis Group

Erscheinungsjahr

2005

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We obtain the Strichartz inequality for any smooth three-dimensional Riemannian manifold (M, g) which is asymptotically conic at infinity and nontrapping, where u is a solution to the Schrödinger equation iu t  + (1/2)Δ M u = 0. The exponent H 1/4 (M) is sharp, by scaling considerations. In particular our result covers asymptotically flat nontrapping manifolds. Our argument is based on the interaction Morawetz inequality introduced by Colliander et al., interpreted here as a positive commutator inequality for the tensor product U(t, z′, z′′): = u(t, z′)u(t, z′′) of the solution with itself. We also use smoothing estimates for Schrödinger solutions including one (proved here) with weight r −1 at infinity and with the gradient term involving only one angular derivative.