# Threshold for Blowup and Stability for Nonlinear Schrödinger Equation with Rotation

@article{Basharat2020ThresholdFB, title={Threshold for Blowup and Stability for Nonlinear Schr{\"o}dinger Equation with Rotation}, author={Nyla Basharat and Hichem Hajaiej and Y. Hu and Shijun Zheng}, journal={arXiv: Analysis of PDEs}, year={2020} }

We consider the focusing NLS with an angular momentum and a harmonic potential, which models Bose-Einstein condensate under a rotating magnetic trap. We give a sharp condition on the global existence and blowup in the mass-critical case. We further consider the stability of such systems via variational method. We determine that at the critical exponent $p=1+4/n$, the mass of $Q$, the ground state for the NLS with zero potential, is the threshold for both finite time blowup and orbital…

## 8 Citations

Remarks on nonlinear Schrödinger equations arising on rotational Bose–Einstein condensates

- Mathematics, PhysicsNonlinear Analysis
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Existence and stability of standing waves for nonlinear Schrödinger equations with a critical rotational speed

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On stability of rotational 2D binary Bose-Einstein condensates

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We consider a two-dimensional nonlinear Schrodinger equation proposed in Physics to model rotational binary Bose-Einstein condensates. The nonlinearity is a logarithmic modification of the usual…

Blowup rate for mass critical rotational
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We consider the blowup rate for blowup solutions to $L^2$-critical, focusing NLS with a harmonic potential and a rotation term. Under a suitable spectral condition we prove that there holds the…

Multiplicity, asymptotics and stability of standing waves for nonlinear Schrödinger equation with rotation

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The Nonexistence of Vortices for Rotating Bose-Einstein Condensates in Non-Radially Symmetric Traps

- Physics, Mathematics
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We consider ground states of rotating Bose-Einstein condensates with attractive interactions in a homogeneous trap $V(x)$ of degree $2$ in $R^2$, which can be non-radially symmetric. For any fixed…

Universal Upper Bound on the Blowup Rate of Nonlinear Schrödinger Equation with Rotation

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In this paper, we prove a universal upper bound on the blowup rate of a focusing nonlinear Schrödinger equation with an angular momentum under a trapping harmonic potential, assuming that the initial…

Global Well-Posedness, Blow-Up and Stability of Standing Waves for Supercritical NLS with Rotation

- Mathematics
- 2020

We consider the focusing mass supercritical nonlinear Schrodinger equation with rotation \begin{equation*}
iu_{t}=-\frac{1}{2}\Delta u+\frac{1}{2}V(x)u-|u|^{p-1}u+L_{\Omega}u,\quad (x,t)\in…

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