Journal of Mathematical Fluid Mechanics

, Volume 12, Issue 1, pp 101–132

Existence of Strong Solutions for Incompressible Fluids with Shear Dependent Viscosities

  • Luigi C. Berselli
  • Lars Diening
  • Michael Růžička
Article

DOI: 10.1007/s00021-008-0277-y

Cite this article as:
Berselli, L.C., Diening, L. & Růžička, M. J. Math. Fluid Mech. (2010) 12: 101. doi:10.1007/s00021-008-0277-y

Abstract.

Certain rheological behavior of non-Newtonian fluids in engineering sciences is often modeled by a power law ansatz with p ∈ (1, 2]. In the present paper the local in time existence of strong solutions is studied. The main result includes also the degenerate case (δ = 0) of the extra stress tensor and thus improves previous results of [L. Diening and M. Růžička, J. Math. Fluid Mech., 7 (2005), pp. 413–450].

Mathematics Subject Classification (2000).

Primary 76A05secondary 35K65, 35Q35, 35B65

Keywords.

Non-Newtonian fluidsshear dependent viscositydegenerate parabolic systemsweak and strong solutionsshifted N-functions

Copyright information

© Birkhäuser Verlag, Basel 2008

Authors and Affiliations

  • Luigi C. Berselli
    • 1
  • Lars Diening
    • 2
  • Michael Růžička
    • 2
  1. 1.Dipartimento di Matematica Applicata “U.Dini”Università di PisaPisaItaly
  2. 2.Institute of Applied MathematicsAlbert-Ludwigs-University FreiburgFreiburgGermany