论文标题
$ l^p $，$ p> 2 $的1D立方非线性schrödinger方程的适应性良好
Well-posedness for the 1D cubic nonlinear Schrödinger equation in $L^p$, $p>2$
论文作者
论文摘要
在本文中，显示了$ 2 <p <4 $的一维立方非线性schrödinger方程，以$ 2 <p <4 $为$ l^p $ spaces的本地供应良好，这在Y.结果，为一类数据建立了局部解决方案理论，该数据比正方形的集成函数衰减较慢。还证明了在$ l^p $的Sobolev空间和Stricharz空间中本地解决方案的规律性属性。
In this paper, local well-posedness is shown for the one dimensional cubic nonlinear Schrödinger equation in $L^p$-spaces for $2<p<4$, which generalizes a classical result for $p=2$ by Y. Tsutsumi and recent work for $1<p<2$ by Y. Zhou. As a consequence, a local theory of solutions is established for a class of data which decay more slowly than square integrable functions. Regularity properties of the local solutions in the $L^p$-based Sobolev spaces and Stricharz spaces are also proved.
