Low-Regularity Integrator for the Davey–Stewartson System: Elliptic-Elliptic Case-Reference-Cited by-同舟云学术

Low-Regularity Integrator for the Davey–Stewartson System: Elliptic-Elliptic Case

Published:2022-05-12 Issue:3 Volume:22 Page:675-684
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Ning Cui¹,Wang Yaohong²^ORCID

Affiliation:

1. School of Financial Mathematics and Statistics , Guangdong University of Finance , Guangzhou , Guangdong 510521 , P. R. China

2. Center for Applied Mathematics , Tianjin University , Tianjin , 300072 , P. R. China

Abstract

Abstract In this paper, we introduce a first-order low-regularity integrator for the Davey–Stewartson system in the elliptic-elliptic case. It only requires the boundedness of one additional derivative of the solution to be first-order convergent. By rigorous error analysis, we show that the scheme provides first-order accuracy in H γ ⁢ ( T d )

H^{\gamma}(\mathbb{T}^{d})

for rough initial data in H γ + 1 ⁢ ( T d )

H^{\gamma+1}(\mathbb{T}^{d})

with γ > d 2

\gamma>\frac{d}{2}

Funder

National Natural Science Foundation of China

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2020-0180/pdf

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