Registered Data

[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.
  • Classification : 65M12, 65M15, 35Q55
  • Format : Talk at Waseda University
  • Author(s) :
    • Lun Ji (Universität Innsbruck)
    • Alexander Ostermann (Universität Innsbruck)
    • Frédéric Rousset (Université Paris-Saclay)
    • Katharina Schratz (Sorbonne Université)