Zeitschrift für angewandte Mathematik und Physik

, Volume 63, Issue 1, pp 191–202

Further mathematical results concerning Burgers fluids and their generalizations

Authors

    • Matematica Aplicada 2 U.P.C.
  • K. R. Rajagopal
    • Mechanical EngineeringTexas A & M University
Article

DOI: 10.1007/s00033-011-0173-9

Cite this article as:
Quintanilla, R. & Rajagopal, K.R. Z. Angew. Math. Phys. (2012) 63: 191. doi:10.1007/s00033-011-0173-9

Abstract

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.

Mathematics Subject Classification (2000)

35K2535Q8676A05

Keywords

Generalized Burgers fluidsEnergy methodsStability

Copyright information

© Springer Basel AG 2011