{"title":"A Numerical Study on Singularity Formation of the 2D Ideal MHD Equations","authors":"Daisuke Hirata","doi":"10.1007/s10440-025-00710-4","DOIUrl":null,"url":null,"abstract":"<div><p>In this note, we study numerically the regularity issue of the ideal MHD equations on the two-dimensional torus. By pseudo-spectral method, we provide evidence that a certain numerical solution is initially regular and eventually very singular in finite time.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"195 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Applicandae Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10440-025-00710-4","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
In this note, we study numerically the regularity issue of the ideal MHD equations on the two-dimensional torus. By pseudo-spectral method, we provide evidence that a certain numerical solution is initially regular and eventually very singular in finite time.
期刊介绍：
Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods.
Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.
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