Dispersive estimates for nonlinear Schrodinger equations with external potentials

Dietze, Charlotte (2021): Dispersive estimates for nonlinear Schrodinger equations with external potentials. In: Journal of Mathematical Physics, Vol. 62, No. 11, 111502

Abstract

We consider the long time dynamics of nonlinear Schrodinger equations with an external potential. More precisely, we look at Hartree type equations in three or higher dimensions with small initial data. We prove an optimal decay estimate, which is comparable to the decay of free solutions. Our proof relies on good control on a high Sobolev norm of the solution to estimate the terms in Duhamel's formula.</p>

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0022-2488
• Language: English