一个偶极量子气体爆破的新准则

A New Blow-up Criterion for Trapped Dipolar Quantum Gases

研究偶极量子气体在部分不稳定区域中爆破的充分条件.通过内插不等式和对非线性项的控制,得到virial恒等式的一个变分刻画,结合粒子在有势垒场中运动的力学类比得到方程在部分不稳定区域中爆破的充分条件.

In this paper,we discuss the sufficient conditions for the collapse of trapped dipole quantum gases in part of the unstable region.A variational characteristic of the virial identity is obtained by the interpolation inequality and the control of nonlinear terms.Combining with the mechanical analogy of particle motion in a potential barrier field,we obtain a sufficient condition for the collapse of the equation.