Abstract
This paper deals with the equations ∇ ·u=o,u′ − νΔu − κΔu′+u · ∇u+∇p=f, describing a Non-Newtonian liquid with velocityu, pressure p under the external forcef. The difference to the Navier-Stokes equations consists in the fact that it is assumed here that the external forcef only has an effect on the volume-element of the liquid after the relaxation-time κ/ν.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literatur
Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II. Comm. Pure Appl. Math. 17, 35–92 (1964).
Kaniel, S., Shinbrot, M.: Smoothness of weak solutions of the Navier-Stokes Equations, Archive Rat. Mech. Anal. 24, 302–324 (1967).
Oskolkov, A.P.: On some nonstationary linear and quasilinear systems occuring in studying the motion of viscous fluids. Boundary value problems of mathematical physics and questions of the theory of functions. 9. Lectures mathematical seminar LOMI 59, 133–177 (1976) (Russian).
Ladyženskaja, O.A.: Funktionalanalytische Untersuchungen der Navier-Stokesschen Gleichungen, Akademie-Verlag: Berlin (1965).
Friedman, A.: Partial Differential Equations. Holt, Rinehart and Winston: New York, Montreal, London, Sydney (1969).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
von Wahl, W. Über das Modell einer Nicht-Newtonschen Flüssigkeit mit Relaxationseigenschaften. Manuscripta Math 22, 131–135 (1977). https://doi.org/10.1007/BF01167856
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01167856