Existence and stability of standing waves for nonlinear Schrödinger equations with a critical rotational speed

van Duong Dinh (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We study the existence and stability of standing waves associated to the Cauchy problem for the nonlinear Schrödinger equation (NLS) with a critical rotational speed and an axially symmetric harmonic potential. This equation arises as an effective model describing the attractive Bose-Einstein condensation in a magnetic trap rotating with an angular velocity. By viewing the equation as NLS with a constant magnetic field and with (or without) a partial harmonic confinement, we establish the existence and orbital stability of prescribed mass standing waves for the equation with masssubcritical, mass-critical, and mass-supercritical nonlinearities. Our result extends a recent work of [Bellazzini-Boussaïd-Jeanjean-Visciglia, Comm. Math. Phys. 353 (2017), no. 1, 229-251], where the existence and stability of standing waves for the supercritical NLS with a partial confinement were established.

Mots clés: 2010 Mathematics Subject Classification. 35A01; 35Q55 Nonlinear Schrödinger equation; Standing waves; Stability; Rotation

Domaines: Equations aux dérivées partielles [math.AP]

van Duong Dinh. Existence and stability of standing waves for nonlinear Schrödinger equations with a critical rotational speed. Letters in Mathematical Physics, 2022, 112 (53). ⟨hal-03520966⟩