Asymptotic stability of steady compressible fluids / Mariarosaria Padula

Auteur: Padula, Mariarosaria (1949-2012) - AuteurType de document: MonographieCollection: Lecture notes in mathematics ; 2024Langue: anglaisPays: AllemagneÉditeur: Berlin : Springer, cop. 2011Description: 1 vol. (XIV-235 p.) ; 24 cm ISBN: 9783642211362 ; br. Résumé: This volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids. It is intended for a wide audience of theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory. The focus is particularly on recent results concerning nonlinear asymptotic stability, which are independent of assumptions about the smallness of the initial data. Of particular interest is the loss of control that sometimes results when steady flows of compressible fluids are upset by large disturbances. The main ideas are illustrated in the context of three different physical problems: (i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous. (ii) An isothermal viscous gas in a domain with free boundaries. (iii) A heat-conducting, viscous polytropic gas. (Source : Springer).Bibliographie: Bibliogr. p. 223-229. Index. Sujets MSC: 76-02 Fluid mechanics -- Research exposition (monographs, survey articles)
76N10 Fluid mechanics -- Compressible fluids and gas dynamics, general -- Existence, uniqueness, and regularity theory
76E30 Fluid mechanics -- Hydrodynamic stability -- Nonlinear effects
35Q35 Partial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with fluid mechanics
80A20 Classical thermodynamics, heat transfer -- Thermodynamics and heat transfer -- Heat and mass transfer, heat flow
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Bibliogr. p. 223-229. Index

This volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids. It is intended for a wide audience of theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory.
The focus is particularly on recent results concerning nonlinear asymptotic stability, which are independent of assumptions about the smallness of the initial data. Of particular interest is the loss of control that sometimes results when steady flows of compressible fluids are upset by large disturbances. The main ideas are illustrated in the context of three different physical problems: (i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous. (ii) An isothermal viscous gas in a domain with free boundaries. (iii) A heat-conducting, viscous polytropic gas. (Source : Springer)

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