{"title":"Onset of Nonlinear Instabilities in Monotonic Viscous Boundary Layers","authors":"D. Bian, E. Grenier","doi":"10.1137/22m1505773","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3703-3719, June 2024. <br/> Abstract. In this paper, we study the nonlinear stability of a shear layer profile for Navier–Stokes equations near a boundary. More precisely, we investigate the effect of cubic interactions on the growth of the linear instability. In the case of the exponential profile, we obtain that the nonlinearity tames the linear instability. We thus conjecture that small perturbations grow until they reach a magnitude [math] only, forming small rolls in the critical layer near the boundary. The mathematical proof of this conjecture is open.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-05-31","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/10.1137/22m1505773","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 3, Page 3703-3719, June 2024. Abstract. In this paper, we study the nonlinear stability of a shear layer profile for Navier–Stokes equations near a boundary. More precisely, we investigate the effect of cubic interactions on the growth of the linear instability. In the case of the exponential profile, we obtain that the nonlinearity tames the linear instability. We thus conjecture that small perturbations grow until they reach a magnitude [math] only, forming small rolls in the critical layer near the boundary. The mathematical proof of this conjecture is open.
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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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