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Further mathematical results concerning Burgers fluids and their generalizations
Quintanilla de Latorre, Ramón; Rajagopal, Kumbakonam
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada
In this paper, we extend the earlier work by Quintanilla and Rajagopal (Math Methods Appl Sci 29: 2133–2147, 2006) and establish qualitative new results for a proper generalization of Burgers’ original work that stems form a general thermodynamic framework. Such fluids have been used to describe the behavior of several geological materials such as asphalt and the earth’s mantle as well as polymeric fluids. We study questions concerning stability, uniqueness and continuous dependence on initial data for the solutions of the flows of these fluids. We show that if certain conditions are not satisfied by the material moduli, the solutions could be unstable. The spatial behavior of the solutions is also analyzed.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica de fluids
Fluid mechanics
Differential equations, Partial
Equacions en derivades parcials
Mecànica de fluids
Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems
Classificació AMS::76 Fluid mechanics::76A Foundations, constitutive equations, rheolog

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