{"title":"On the equations of thin shock layer theory","authors":"Manuel Núñez","doi":"10.1016/j.ijnonlinmec.2024.104921","DOIUrl":null,"url":null,"abstract":"<div><div>The theory of high Mach number flows creating a thin layer between a shock wave and a delta wing surface rests on a certain functional equation or its associated differential one, both of which are nonstandard and the existence of solutions cannot be guaranteed. There exists a free parameter within these equations in the form of the shape of the wing, about which we wish to obtain necessary conditions for a thin shock layer to exist. We get some direct estimates in terms of bounds on the side flow at the initial condition, as well as some indirect ones related to the regularity of the shock wave, which is itself linked to the energy of the flow.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104921"},"PeriodicalIF":2.8000,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Non-Linear Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020746224002865","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The theory of high Mach number flows creating a thin layer between a shock wave and a delta wing surface rests on a certain functional equation or its associated differential one, both of which are nonstandard and the existence of solutions cannot be guaranteed. There exists a free parameter within these equations in the form of the shape of the wing, about which we wish to obtain necessary conditions for a thin shock layer to exist. We get some direct estimates in terms of bounds on the side flow at the initial condition, as well as some indirect ones related to the regularity of the shock wave, which is itself linked to the energy of the flow.
期刊介绍：
The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear.
The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas.
Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.
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