Abstract
We consider the focusing mass supercritical nonlinear Schrödinger equation with rotation
where \(N=2\) or 3 and V(x) is an anisotropic harmonic potential. Here \(L_{\Omega }\) 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.
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The authors would like to express their sincere thanks to the referees for useful comments and suggestions that improved the paper.
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Ardila, A.H., Hajaiej, H. Global Well-Posedness, Blow-Up and Stability of Standing Waves for Supercritical NLS with Rotation. J Dyn Diff Equat 35, 1643–1665 (2023). https://doi.org/10.1007/s10884-021-09976-2
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DOI: https://doi.org/10.1007/s10884-021-09976-2