Methods and Applications of Analysis

Volume 28 (2021)

Number 3

Special issue dedicated to Professor Ling Hsiao on the occasion of her 80th birthday, Part II

Guest editors: Qiangchang Ju (Institute of Applied Physics and Computational Mathematics, Beijing), Hailiang Li (Capital Normal University, Beijing), Tao Luo (City University of Hong Kong), and Zhouping Xin (Chinese University of Hong Kong)

Convergence rates of the singular limit for equatorial shallow-water dynamics

Pages: 387 – 400

DOI: https://dx.doi.org/10.4310/MAA.2021.v28.n3.a9

Authors

Song Jiang (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Qiangchang Ju (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Xin Xu (School of Mathematical Sciences, Ocean University of China, Qingdao, China)

Abstract

We study the singular limit of the equatorial shallow-water system which describes the motion of the atmosphere/ocean in the equatorial zone. Based on the convergence result of Dutrifoy, Majda and Schochet [Comm. Pure Appl. Math., 2009, 62(3): 322–333], we further obtain the convergence rate estimates of the solutions in the case of well-prepared initial data.

Keywords

equatorial shallow-water system, singular limit, convergence rates

2010 Mathematics Subject Classification

35B25, 35L45, 35Q35

Full Text (PDF format)

This research was supported by the NSFC-ISF joint research program (Grant No. 11761141008). The research of Jiang was supported by NSFC (Grant No. 11631008), and National Key R&D Program (2020YFA0712200), National Key Project (GJXM92579) and the Sino-German Science Center (Grant No. GZ1465). Ju was supported by NSFC (Grant No. 12070144). Xu was supported by Project funded by China Postdoctoral Science Foundation (Grant No. 2021T140633 and 2021M693028), NSFC (Grant No. 12001506) and the Natural Science Foundation of Shandong Province (Grant No. ZR2020QA014).

Received 17 February 2020

Accepted 11 August 2020

Published 10 June 2022