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Global Well-Posedness, Blow-Up and Stability of Standing Waves for Supercritical NLS with Rotation.
- Source :
-
Journal of Dynamics & Differential Equations . Jun2023, Vol. 35 Issue 2, p1643-1665. 23p. - Publication Year :
- 2023
-
Abstract
- We consider the focusing mass supercritical nonlinear Schrödinger equation with rotation i u t = - 1 2 Δ u + 1 2 V (x) u - | u | p - 1 u + L Ω u , (x , t) ∈ R N × R , where N = 2 or 3 and V(x) is an anisotropic harmonic potential. Here L Ω is the quantum mechanical angular momentum operator. We establish conditions for global existence and blow-up in the energy space. Moreover, we prove strong instability of standing waves under certain conditions on the rotation and the frequency of the wave. Finally, we construct orbitally stable standing waves solutions by considering a suitable local minimization problem. Those results are obtained for nonlinearities which are L 2 -supercritical. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10407294
- Volume :
- 35
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Dynamics & Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 163914505
- Full Text :
- https://doi.org/10.1007/s10884-021-09976-2