Another computer-assisted proof of unimodality of solutions for Proudman–Johnson equation-Reference-Cited by-同舟云学术

Another computer-assisted proof of unimodality of solutions for Proudman–Johnson equation

Published:2024-01-03 Issue:2 Volume:41 Page:1013-1032
ISSN:0916-7005
Container-title:Japan Journal of Industrial and Applied Mathematics
language:en
Short-container-title:Japan J. Indust. Appl. Math.

Author:

Watanabe Yoshitaka^ORCID,Miyaji Tomoyuki

Abstract

AbstractThis paper presents a computer-assisted proof of the existence and unimodality of steady-state solutions for the Proudman–Johnson equation which is representative of two-dimensional fluid flow. The proposed approach is based on an infinite-dimensional fixed-point theorem with interval arithmetic, and is another proof by Miyaji and Okamoto (Jpn J Ind Appl Math 36:287–298, 2019). Verification results show the validity of both proofs.

Funder

Japan Society for the Promotion of Science London

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s13160-023-00639-x.pdf

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