论文标题
带有二次非线性$ \ overline {u}^2 $的周期性非线性schrödinger方程的本地良好性
Local well-posedness of the periodic nonlinear Schrödinger equation with a quadratic nonlinearity $\overline{u}^2$ in negative Sobolev spaces
论文作者
论文摘要
我们研究了非线性schrödinger方程（NLS）的低规律性局部良好性，其二维非线性$ \ edline {u}^2 $，在一维和二维Tori上构成。尽管相关的双线性估计值相对于$ x^{s，b} $ - 众所周知，当规则性$ s $低于某个阈值时，众所周知，空间会失败，但我们通过对$ x^{s，b} $ space引入$ x^{s^{s，b} $ space来建立如此低规律性的本地良好性。
We study low regularity local well-posedness of the nonlinear Schrödinger equation (NLS) with the quadratic nonlinearity $\overline{u}^2$, posed on one-dimensional and two-dimensional tori. While the relevant bilinear estimate with respect to the $X^{s, b}$-space is known to fail when the regularity $s$ is below some threshold value, we establish local well-posedness for such low regularity by introducing modifications on the $X^{s, b}$-space.
