{"title":"可压缩介质Navier-Stokes方程的冲击剖面","authors":"Chueh-Hsin Chang, Tai-Ping Liu","doi":"10.1142/s0219891623500157","DOIUrl":null,"url":null,"abstract":"We construct the viscous profile of the Navier–Stokes equations for compressible media under certain sufficient local hypotheses of the constitutive relation. Our result applies to shocks of arbitrary strength and generalizes the classical work of Gilbarg for the convex constitutive relation of Bethe–Weyl.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Shock profiles of Navier–Stokes equations for compressible medium\",\"authors\":\"Chueh-Hsin Chang, Tai-Ping Liu\",\"doi\":\"10.1142/s0219891623500157\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct the viscous profile of the Navier–Stokes equations for compressible media under certain sufficient local hypotheses of the constitutive relation. Our result applies to shocks of arbitrary strength and generalizes the classical work of Gilbarg for the convex constitutive relation of Bethe–Weyl.\",\"PeriodicalId\":50182,\"journal\":{\"name\":\"Journal of Hyperbolic Differential Equations\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Hyperbolic Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219891623500157\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Hyperbolic Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219891623500157","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Shock profiles of Navier–Stokes equations for compressible medium
We construct the viscous profile of the Navier–Stokes equations for compressible media under certain sufficient local hypotheses of the constitutive relation. Our result applies to shocks of arbitrary strength and generalizes the classical work of Gilbarg for the convex constitutive relation of Bethe–Weyl.
期刊介绍：
This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in:
Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions.
Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc.
Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations.
Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc.
General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations.
Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.
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