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Low-Regularity Integrator for the Davey–Stewartson II System

Ning, Cui ; Kou, Xiaomin ; Wang, Yaohong

Journal of scientific computing, 2024-04, Vol.99 (1), p.10, Article 10 [Periódico revisado por pares]

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Título:
Low-Regularity Integrator for the Davey–Stewartson II System
Autor: Ning, Cui ; Kou, Xiaomin ; Wang, Yaohong
Assuntos: Algorithms ; Computational Mathematics and Numerical Analysis ; Convergence ; Error analysis ; Fast Fourier transformations ; Fluid mechanics ; Fourier transforms ; Integrators ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Methods ; Regularity ; Theoretical
É parte de: Journal of scientific computing, 2024-04, Vol.99 (1), p.10, Article 10
Descrição: We consider the Davey–Stewartson system in the hyperbolic–elliptic case (DS-II) in two dimensional case. It is a mass-critical equation, and was proved recently by Nachman et al. (Invent Math 220(2):395–451, 2020) the global well-posedness and scattering in L 2 . In this paper, we give the numerical study on this model and construct a first order low-regularity integrator for the DS-II in the periodic case. It only requires the boundedness of one additional derivative of the solution to get the first order convergence. The Fast Fourier Transform is exploited to speed up the numerical implementation. By rigorous error analysis, we prove that the numerical scheme provides first order convergence in H γ ( T 2 ) for rough initial data in H γ + 1 ( T 2 ) with γ > 1 . The optimality of the convergence is conformed by numerical experience.
Editor: New York: Springer US
Idioma: Inglês

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