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半耗散格点Schr？dinger方程组的统计解与Liouville型定理
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Abstract:
本文研究了半耗散格点非线性Schr？dinger方程组解的拉回渐近行为及其概率分布。该方程组描述带有杂质的Bose-Einstein浓缩模型，模型中的Bose波函数具有耗散性，杂质波函数的能量守恒。作者首先证明该问题的整体适定性，然后研究Bose波函数在适当意义下拉回吸引子的存在性，接着应用该拉回吸引子和广义Banach极限构造统计解，并证明统计解满足Liouville型定理。
In this paper, the pullback asymptotic behavior of solutions to the nonlinear Schr？dinger system of equations with semi-dissipative lattices and their probability distributions are studied. The equations describe the Bose-Einstein condensation model with impurities, in which the Bose wave function is dissipative, and the energy of the impurity wave function is conserved. The authors first prove the global well-posed of the problem and then investigate the existence of a pullback attractor for the Bose wave function in a suitable sense. The authors then apply the pullback attractor and the generalized Banach limit to construct a statistical solution and show that the statistical solution satisfies the Liouville-type theorem.
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