论文标题
圆柱形对称偶极bose-Einstein冷凝物的动力崩溃
Dynamical collapse of cylindrical symmetric Dipolar Bose-Einstein condensates
论文作者
论文摘要
我们研究了圆柱对称解的奇异性形成，描述了描述偶极玻色 - 内斯坦冷凝物的毛pitaevskii方程。我们证明，最初数据引起的解决方案低于基态能量，并且不会在有限的时间内散布崩溃。证明我们的结果的主要工具是基态能量的变异表征，适合圆柱形对称函数的局部病毒身份，以及涉及Riesz变换功率的操作员的一般积分和尖端估计值。
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.
