Fourth Order Schrödinger Equation with Mixed Dispersion on Certain Cartan-Hadamard Manifolds

Autor: Jean-Baptiste Casteras, Ilkka Holopainen
Rok vydání: 2022
Předmět:
Zdroj: Journal of Dynamics and Differential Equations.
ISSN: 1572-9222
1040-7294
DOI: 10.1007/s10884-022-10197-4
Popis: We study the fourth order Schr\"odinger equation with mixed dispersion on an $N$-dimensional Cartan-Hadamard manifold. At first, we focus on the case of the hyperbolic space. Using the fact that there exists a Fourier transform on this space, we prove the existence of a global solution to our equation as well as scattering for small initial data. Next, we obtain weighted Strichartz estimates for radial solutions on a large class of rotationally symmetric manifolds by adapting the method of Banica and Duyckaerts (Dyn. Partial Differ. Equ., 07). Finally, we give a blow-up result for a rotationally symmetric manifold relying on a localized virial argument.
Comment: To appear in Journal of Dynamics and Differential Equations
Databáze: OpenAIRE
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