柱对称偶极玻色-爱因斯坦凝聚体的动力学坍缩
Dynamical collapse of cylindrical symmetric Dipolar Bose-Einstein condensates
摘要：
本文研究了描述偶极玻色-爱因斯坦凝聚体的Gross-Pitaevskii方程柱对称解的奇点形成。我们证明了解决方案所产生的初始数据的能量低于基态的能量，不分散崩溃在有限时间内。证明我们结果的主要工具是基态能量的变分表征，合适的局部维里身份的圆柱对称函数，和一般的积分和逐点估计涉及权力的里斯变换运营商。
英文摘要：
We study the formation of singularities for cylindrical symmetric solutions to the Gross-Pitaevskii equation describing a dipolar Bose-Einstein condensate. We prove that solutions arising from initial data with energy below the energy of the Ground State and that do not scatter collapse in finite time. The main tools to prove our result are the variational characterization of the Ground State energy, suitable localized virial identities for cylindrical symmetric functions, and general integral and pointwise estimates for operators involving powers of the Riesz transforms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
