论文标题
一维非线性schrödinger方程的几乎确定散射
Almost sure scattering for the one dimensional nonlinear Schrödinger equation
论文作者
论文摘要
我们考虑一维非线性schrödinger方程，其非线性$ p> 1 $。我们对初始数据的空间进行了衡量标准，我们描述了线性schrödinger流的非微不足道进化，我们表明它们的非线性进化对于这种线性演化是绝对连续的。我们从此精确描述中推导出该方程式的全球适合性，价格为$ p> 1 $，零售价为$ p> 3 $。据我们所知，这是对准不变措施的描述允许对非线性进化获得定量渐近级（此处散射属性）的第一次情况。
We consider the one-dimensional nonlinear Schrödinger equation with a nonlinearity of degree $p>1$. We exhibit measures on the space of initial data for which we describe the non trivial evolution by the linear Schrödinger flow and we show that their nonlinear evolution is absolutely continuous with respect to this linear evolution. We deduce from this precise description the global well-posedness of the equation for $p>1$ and scattering for $p>3$. To the best of our knowledge, it is the first occurence where the description of quasi-invariant measures allows to get quantitative asymptotics (here scattering properties) for the nonlinear evolution.
