Summary
In this work an examination of the Saffman model for the flow of a dusty gas in a bounded region is conducted. In particular growth properties of the solutions to the nonlinear equations of motion for the model will be studied using energy and logarithmic convexity arguments.
Zusammenfassung
In der vorliegenden Arbeit wird die Wachstumsfrage von Lösungen des Saffmanschen Modelles für die Strömung eines staubgefüllten Gases mit Hilfe von Methoden der Energie und der logarithmischen Konvexität geprüft.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. S. Crooke,On Two Inequalities of the Sobelev Type, Applicable Analysis (to appear).
R. H. Dyer andD. E. Edmunds,On the Regularity of Solutions of the Navier-Stokes Equations, J. London Math. Soc.44, 93 (1969).
H. Fujita andT. Kato,On the Navier-Stokes Initial Value Problem I, Arch. Ration. Mech. Anal.16, 269 (1964).
D. D. Joseph,Nonlinear Stability of the Boussinesq Equations by the Method of Energy, Arch. Ration. Mech. Anal.22, 163 (1966).
F. P. Kazakevich andA. M. Krapivin,Investigations of Heat Transfer and Aerodynamical Resistance in Tube Assemblies when the Flow of Gas in Dustladen (in Russian), Izv. Vyssh. Uchebn. Zavedenii. Energetika #1, 101 (1958).
R. J. Knops andL. E. Payne,Uniqueness in Classical Elastodynamics, Arch. Ration. Mech. Anal.27, 349 (1968).
R. J. Knops andL. E. Payne,On the Stability of Solutions of the Navier-Stokes Equations Backward in Time, Arch. Ration. Mech. Anal.29, 331 (1968).
O. A. Ladyzhenskaya,The Mathematical Theory of Viscous Incompressible Flow (Gordon and Breach, New York 1963).
H. A. Levine,Convexity and Differential Inequalities in Hilbert Space, Ph. D. Thesis (Cornell University, Ithaca N.Y. 1968).
D. H. Michael,The Stability of Plane Poiseuille Flow of a Dusty Gas, J. Fluid Mech.18, 19 (1964).
D. H. Michael,The Steady Motion of a Sphere in a Dusty Gas, J. Fluid Mech.31, 175 (1968).
L. E. Payne,Uniqueness Criteria for Steady State Solutions of the Navier-Stokes Equations, Atti. Simp. Inter. Appl. dell'Anal. alla Fisica Mat. Cagliari-Sassari1964, 133.
L. E. Payne,On Some Non-well Posed Problems for Partial Differential Equations, Numerical Solutions of Non-linear Differential Equations (John Wiley & Sons, New York 1964).
L. E. Payne,Isoperimetric Inequalities and Their Applications, SIAM Review9, 453 (1967).
P. G. Saffman,On the Stability of Laminar Flow of a Dusty Gas, J. Fluid Mech.13, 120 (1962).
J. Serrin,On the Stability of Viscous Fluid Flow, Arch. Ration. Mech. Anal.3, 1 (1959).
J. Serrin,The Initial Value Problem for the Navier-Stokes Equations, Proc. Symp. Non-linear Problems (Univ. of Wisconsin, 1963), p. 69.
W. T. Sproull,Viscosity of Dusty Gases, Nature190, 976 (1961).
C. E. Weatherburn,Differential Geometry in Three Dimensions, Vol. II (Cambridge Univ. Press, Cambridge 1930).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Crooke, P.S. On growth properties of solutions of the saffman dusty gas model. Journal of Applied Mathematics and Physics (ZAMP) 23, 182–200 (1972). https://doi.org/10.1007/BF01593083
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01593083