{"title":"Higher Regularity for Entropy Solutions of Conservation Laws with Geometrically Constrained Discontinuous Flux","authors":"S. S. Ghoshal, S. Junca, A. Parmar","doi":"10.1137/23m1604199","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 6121-6136, October 2024. <br/> Abstract. For the Burgers’ equation, the entropy solution becomes instantly [math] with only [math] initial data. For conservation laws with genuinely nonlinear discontinuous flux, it is well known that the [math] regularity of entropy solutions is lost. Recently, this regularity has been proved to be fractional with [math]. Moreover, for less nonlinear flux, the solution still has a fractional regularity [math]. The resulting general rule is that the regularity of entropy solutions for a discontinuous flux is less than for a smooth flux. In this paper, an optimal geometric condition on the discontinuous flux is used to recover the same regularity as for the smooth flux with the same kind of nonlinearity.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1604199","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 6121-6136, October 2024. Abstract. For the Burgers’ equation, the entropy solution becomes instantly [math] with only [math] initial data. For conservation laws with genuinely nonlinear discontinuous flux, it is well known that the [math] regularity of entropy solutions is lost. Recently, this regularity has been proved to be fractional with [math]. Moreover, for less nonlinear flux, the solution still has a fractional regularity [math]. The resulting general rule is that the regularity of entropy solutions for a discontinuous flux is less than for a smooth flux. In this paper, an optimal geometric condition on the discontinuous flux is used to recover the same regularity as for the smooth flux with the same kind of nonlinearity.
期刊介绍：
SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena.
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Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.
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