Local Well-Posedness to the Magneto-Micropolar Boundary Layer Equations in Gevrey Space

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-12-20 DOI:10.1002/mma.10637

Zhong Tan, Mingxue Zhang

{"title":"Local Well-Posedness to the Magneto-Micropolar Boundary Layer Equations in Gevrey Space","authors":"Zhong Tan, Mingxue Zhang","doi":"10.1002/mma.10637","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>We study the boundary layer equations for two-dimensional magneto-micropolar boundary layer system and establish the existence and uniqueness of solutions in the Gevrey function space without any structural assumption, with Gevrey index \n<span></span><math>\n <semantics>\n <mrow>\n <mi>σ</mi>\n <mo>∈</mo>\n <mo>(</mo>\n <mn>1</mn>\n <mo>,</mo>\n <mfrac>\n <mrow>\n <mn>3</mn>\n </mrow>\n <mrow>\n <mn>2</mn>\n </mrow>\n </mfrac>\n <mo>]</mo>\n </mrow>\n <annotation>$$ \\sigma \\in \\left(1,\\frac{3}{2}\\right] $$</annotation>\n </semantics></math>. Inspired by the abstract Cauchy-Kovalevskaya theorem, our proof is based on a new cancellation mechanism in the system to overcome the difficulties caused by the loss of derivatives. Our results improve the classical local well-posedness results presented in a previous study, specifically for cases where the initial data are analytic in the \n<span></span><math>\n <semantics>\n <mrow>\n <mi>x</mi>\n </mrow>\n <annotation>$$ x $$</annotation>\n </semantics></math>-variable.</p>\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5790-5802"},"PeriodicalIF":2.1000,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10637","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

We study the boundary layer equations for two-dimensional magneto-micropolar boundary layer system and establish the existence and uniqueness of solutions in the Gevrey function space without any structural assumption, with Gevrey index $σ \in (1, \frac{3}{2}]$ . Inspired by the abstract Cauchy-Kovalevskaya theorem, our proof is based on a new cancellation mechanism in the system to overcome the difficulties caused by the loss of derivatives. Our results improve the classical local well-posedness results presented in a previous study, specifically for cases where the initial data are analytic in the $x$ -variable.

查看原文本刊更多论文

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.