论文标题
NLS分裂方案的规律性较低的错误估计值
Error estimates at low regularity of splitting schemes for NLS
论文作者
论文摘要
我们研究了用于立方非线性schrödinger方程的过滤谎言分裂方案。我们通过使用离散的波尔加因空间以低规律性建立错误估计。这使我们能够以$ 0 <s <1 $克服标准稳定性限制到平滑Sobolev空格，并使用索引$ s> 1/2 $来处理$ H^s $中的数据。更确切地说，我们证明在这种规律性的级别上，$ l^2 $中的订单$τ^{s/2} $的收敛速率。
We study a filtered Lie splitting scheme for the cubic nonlinear Schrödinger equation. We establish error estimates at low regularity by using discrete Bourgain spaces. This allows us to handle data in $H^s$ with $0<s<1$ overcoming the standard stability restriction to smooth Sobolev spaces with index $s>1/2$ . More precisely, we prove convergence rates of order $τ^{s/2}$ in $L^2$ at this level of regularity.
