{"title":"Magneto-hydrodynamic equations and parametric flag microlocal quantities at binary time interval","authors":"Zhenzhen Lou, Qixiang Yang, Jianxun He","doi":"10.1002/mma.10386","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we establish the well-posedness of the Cauchy problem for incompressible magneto-hydrodynamic equations by using parametric Meyer wavelets. The velocity field and magnetic field are expanded according to parametric wavelets given by a discrete set of thresholds. The evolution of these two types of fields is described by the relationship of parameterized flag microlocal quantities over binary time intervals. The corresponding iteration space is defined by the decay of the single norm, and the single norm is defined by the parametric flag microlocal quantities at a set of binary time interval.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"1311-1337"},"PeriodicalIF":1.8000,"publicationDate":"2024-08-07","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.10386","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
In this paper, we establish the well-posedness of the Cauchy problem for incompressible magneto-hydrodynamic equations by using parametric Meyer wavelets. The velocity field and magnetic field are expanded according to parametric wavelets given by a discrete set of thresholds. The evolution of these two types of fields is described by the relationship of parameterized flag microlocal quantities over binary time intervals. The corresponding iteration space is defined by the decay of the single norm, and the single norm is defined by the parametric flag microlocal quantities at a set of binary time interval.
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.
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