An Explicit Filtered Lie Splitting Scheme for the Original Zakharov System with Low Regularity Error Estimates in All Dimensions

In this talk, we present low-regularity numerical schemes for nonlinear dispersive equations, with a particular focus on the Zakharov system (ZS) and the “good” Boussinesq (GB) equation. These models exhibit strong nonlinear interactions and are known to pose significant analytical and numerical challenges when the solution has limited regularity.

We concentrate on our recent results for the Zakharov system, where we construct and analyze an explicit filtered Lie splitting scheme applied directly to its original coupled form. This method successfully overcomes the essential difficulty of derivative loss in the nonlinear terms, which not only obstructs low-regularity analysis, but has long prevented rigorous error estimates for explicit Lie splitting schemes based directly on the original Zakharov system. By developing multilinear estimates in discrete Bourgain spaces, we rigorously prove the first explicit low-regularity error estimate for the original Zakharov system, and also the first such result for a coupled system within the Bourgain framework. The analytical strategy developed here can also be extended to other dispersive equations with derivative loss, offering a way to overcome both low-regularity difficulties and the fundamental obstacle posed by derivative-loss nonlinearities. Numerical experiments confirm the theoretical predictions.

• Speaker: Hang Li (Sorbonne Université)
• Thursday 01 May 2025, 15:00–16:00
• Venue: Centre for Mathematical Sciences, MR14.
• Series: Applied and Computational Analysis; organiser: Georg Maierhofer.