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Article Dans Une Revue Journal of Dynamics and Differential Equations Année : 2022

The 3D nonlinear Schrödinger equation with a constant magnetic field revisited

van Duong Dinh
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Résumé

In this paper, we revisit the Cauchy problem for the three dimensional nonlinear Schrödinger equation with a constant magnetic field. We first establish sufficient conditions that ensure the existence of global in time and finite time blow-up solutions. In particular, we derive sharp thresholds for global existence versus blow-up for the equation with mass-critical and mass-supercritical nonlinearities. We next prove the existence and orbital stability of normalized standing waves which extend the previous known results to the mass-critical and mass-supercritical cases. To show the existence of normalized solitary waves, we present a new approach that avoids the celebrated concentrationcompactness principle. Finally, we study the existence and strong instability of ground state standing waves which greatly improve the previous literature.
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Dates et versions

hal-03520972 , version 1 (11-01-2022)

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  • HAL Id : hal-03520972 , version 1

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van Duong Dinh. The 3D nonlinear Schrödinger equation with a constant magnetic field revisited. Journal of Dynamics and Differential Equations, 2022. ⟨hal-03520972⟩
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