论文标题
几乎可以确保具有高阶操作员的立方非线性Schrodinger方程的本地良好性
Almost sure local well-posedness for cubic nonlinear Schrodinger equation with higher order operators
论文作者
论文摘要
在本文中，我们研究了立方schrödinger方程的本地良好性：\ [（i \ partial_t- \ \ \ \ \ mathscr {l}） $σ\ geq 2 $。使用方向空间中的估计值，我们改进并扩展了标准Schrödinger方程（即$ \ Mathscr {l} =δ$）的已知结果，并在一般$ \ Mathscr {l} $的自然假设下获得结果。
In this paper, we study the local well-posedness of the cubic Schrödinger equation: \[ (i \partial_t - \mathscr{L}) u = \pm |u|^2 u \quad \text{ on } I \times \mathbb{R}^d, \] with randomized initial data, and $\mathscr{L}$ being an operator of degree $σ\geq 2$. Using estimates in directional spaces, we improve and extend known results for the standard Schrödinger equation (i.e. $\mathscr{L} = Δ$) to any dimension and obtain results under natural assumptions for general $\mathscr{L}$.
