We establish sharp-in-time kernel and dispersive estimates for the Schrödinger equation on non-compact Riemannian symmetric spaces of any rank. Due to the particular geometry at infinity and the Kunze-Stein phenomenon, these properties are more pronounced in large time and enable us to prove the global-in-time Strichartz inequality for a larger family of admissible couples than in the Euclidean case. Consequently, we obtain the global well-posedness for the corresponding semilinear equation with lower regularity data and some scattering properties for small powers which are known to fail in the Euclidean setting. The crucial kernel estimates are achieved by combining the stationary phase method based on a subtle barycentric decomposition, a subordination formula of the Schrödinger group to the wave propagator and an improved Hadamard parametrix.

Anker, J., Meda, S., Pierfelice, V., Vallarino, M., Zhang, H. (2023). Schrödinger equation on non-compact symmetric spaces. JOURNAL OF DIFFERENTIAL EQUATIONS, 356(25 May 2023), 163-187 [10.1016/j.jde.2023.02.003].

Schrödinger equation on non-compact symmetric spaces

Meda S.;
2023

Abstract

We establish sharp-in-time kernel and dispersive estimates for the Schrödinger equation on non-compact Riemannian symmetric spaces of any rank. Due to the particular geometry at infinity and the Kunze-Stein phenomenon, these properties are more pronounced in large time and enable us to prove the global-in-time Strichartz inequality for a larger family of admissible couples than in the Euclidean case. Consequently, we obtain the global well-posedness for the corresponding semilinear equation with lower regularity data and some scattering properties for small powers which are known to fail in the Euclidean setting. The crucial kernel estimates are achieved by combining the stationary phase method based on a subtle barycentric decomposition, a subordination formula of the Schrödinger group to the wave propagator and an improved Hadamard parametrix.
Articolo in rivista - Articolo scientifico
Dispersive property; Non-compact symmetric space; Pointwise kernel estimate; Semilinear Schrödinger equation; Strichartz inequality;
English
8-feb-2023
2023
356
25 May 2023
163
187
none
Anker, J., Meda, S., Pierfelice, V., Vallarino, M., Zhang, H. (2023). Schrödinger equation on non-compact symmetric spaces. JOURNAL OF DIFFERENTIAL EQUATIONS, 356(25 May 2023), 163-187 [10.1016/j.jde.2023.02.003].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/451174
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