论文标题
衍生品非线性schrödinger方程的标准通货膨胀
Norm inflation for the derivative nonlinear Schrödinger equation
论文作者
论文摘要
在本说明中，我们研究了一维环境中导数非线性schrödinger方程（DNLS）的不良性问题。更确切地说，通过使用Duhamel公式的三元Quinary Tree扩展，我们证明了仪表DNL的（缩放）临界规律性下方的Sobolev空间中的标准通胀。由于已知DNL在$ l^2（\ Mathbb {r}）$中，因此这种不适的结果是尖锐的。我们方法的主要新颖性是通过精心选择的初始数据来控制五重非线性从立方非线性中的衍生损失。
In this note, we study the ill-posedness problem for the derivative nonlinear Schrödinger equation (DNLS) in the one-dimensional setting. More precisely, by using a ternary-quinary tree expansion of the Duhamel formula we prove norm inflation in Sobolev spaces below the (scaling) critical regularity for the gauged DNLS. This ill-posedness result is sharp since DNLS is known to be globally well-posed in $L^2(\mathbb{R})$. The main novelty of our approach is to control the derivative loss from the cubic nonlinearity by the quintic nonlinearity with carefully chosen initial data.
