论文标题
一维毛毛虫方程的保守能量：低规律性案例
Conserved energies for the one dimensional Gross-Pitaevskii equation: low regularity case
论文作者
论文摘要
我们为一维的pitaevskii方程构建了一个保守的能量家族，但是在低规律性的情况下（在\ cite {kl}中，我们在高规律性情况下构建了保守的能量）。这可以借助正规化程序以及对有限能源空间的拓扑结构的研究。研究了$ \ r/2π\ z $中的值的渐近（正则保守）相变。我们还在有限能量空间的通用覆盖空间上构造了一个保守的数量，即恢复归一化的动量$ h_1 $（请参见定理\ ref {thm：e1}）。
We construct a family of conserved energies for the one dimensional Gross-Pitaevskii equation, but in the low regularity case (in \cite{KL} we have constructed conserved energies in the high regularity situation). This can be done thanks to regularization procedures and a study of the topological structure of the finite-energy space. The asymptotic (regularised conserved) phase change on the real line with values in $ \R/2π\Z$ is studied. We also construct a conserved quantity, the renormalized momentum $H_1$ (see Theorem \ref{thm:E1}), on the universal covering space of the finite-energy space.
