[01986] Low regularity time integration of NLS via discrete Bourgain spaces
Session Time & Room : 3E (Aug.23, 17:40-19:20) @E604
Type : Contributed Talk
Abstract : We study a filtered Lie splitting scheme for the cubic periodic nonlinear Schrödinger equation on the torus $\mathbb{T}^d$ with $d\geq1$. This scheme overcomes the standard stability restriction $s>\frac d2$ in Sobolev spaces $H^s(\mathbb{T}^d)$ and now allows us to handle initial data in $H^s$ for $s>0$ when $d=1,2$ and $s>\frac d2-1$ when $d\geq3$. Moreover, we establish low regularity error estimates in discrete Bourgain spaces, and prove convergence of order $\tau^{\frac s2}$ in $L^2(\mathbb{T}^d)$, where $\tau$ denotes the time step size.
