论文标题
旋转的非线性schrödinger方程的多重性，渐近和稳定性
Multiplicity, asymptotics and stability of standing waves for nonlinear Schrödinger equation with rotation
论文作者
论文摘要
在本文中，我们研究了具有规定的质量$ C> 0 $的多样性，渐近性和稳定性，用于非线性Schrödinger方程，并在Bose-Einstein Conensation中产生的质量优化状态中旋转。在适当限制旋转频率的情况下，通过搜索质量表上的相应能量功能的临界点，我们获得了局部最小化$ u_c $和Mountain Pass pass解决方案$ \ hat {u} _c $。在相关参数的适当假设下的％。此外，我们表明$ u_c $是小质量$ c> 0 $的基态状态，并将最小化器的质量崩溃行为描述为$ c \ to 0 $，而$ \ hat {u} _c $是一种激动的状态。最后，我们证明了与$ u_c $相关的常驻波是稳定的。请注意，开拓性的作品\ cite {amsc，shyz}意味着该模型的解决方案有限的时间爆炸发生在质量质量的环境中，因此，在本文中，我们在本文中获得了新的稳定性结果。本文的主要贡献是将主要结果扩展到\ cite {jesp，gylw}，涉及相同的模型，从质量 - 婚礼和质量批判性制度到涵盖了最相关的情况。
In this article, we study the multiplicity, asymptotics and stability of standing waves with prescribed mass $c>0$ for nonlinear Schrödinger equation with rotation in the mass-supercritical regime arising in Bose-Einstein condensation. Under suitable restriction on the rotation frequency, by searching critical points of the corresponding energy functional on the mass-sphere, we obtain a local minimizer $u_c$ and a mountain pass solution $\hat{u}_c$. %under suitable assumptions on the related parameters. Furthermore, we show that $u_c$ is a ground state for small mass $c>0$ and describe a mass collapse behavior of the minimizers as $c\to 0$, while $\hat{u}_c$ is an excited state. Finally, we prove that the standing wave associated with $u_c$ is stable. Notice that the pioneering works \cite{aMsC,shYZ} imply that finite time blow-up of solutions to this model occurred in the mass-supercritical setting, therefore, we in the present paper obtain a new stability result. The main contribution of this paper is to extend the main results in \cite{JeSp,gYlW} concerning the same model from mass-subcritical and mass-critical regimes to mass-supercritical regime, where the physically most relevant case is covered.
