Interior differentiability of weak solutions to the equations of stationary motion of a class of non-Newtonian fluids

Journal of Mathematical Fluid Mechanics

Volumn 7, Issue 2, 2005, Pages 298-313

  Naumann, J ^a   Wolf, J ^a  

^a HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Difference estimates of weak solutions; Fractional differentiability; Non Newtonian fluids

Indexed keywords

EQUATIONS OF MOTION; FUNCTIONS; MATHEMATICAL MODELS; SHEAR FLOW; STRESS ANALYSIS; TENSORS; THEOREM PROVING;

DIFFERENCE ESTIMATES OF WEAK SOLUTIONS; FRACTIONAL DIFFERENTIABILITY; POWER LAW MODEL; STATIONARY MOTION;

NON NEWTONIAN LIQUIDS;

NON-NEWTONIAN FLUID;

EID: 21244462729     PISSN: 14226928     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00021-004-0120-z     Document Type: Article

References (16)

1. R. A. ADAMS, Sobolev spaces, Academic Press, Boston, 1978.
2. G. ASTARITA and G. MARRUCCI, Principles of non-Newtonian fluid mechanics, McGraw-Hill, London, New York 1974.
3. G. K. BATCHELOR, An introduction to fluid mechanics, Cambridge Univ. Press, Cambridge, 1967.
4. R. B. BIRD, R. C. ARMSTRONG and O. HASSAGER, Dynamics of polymer liquids. Vol. 1: Fluid mechanics, 2nd ed., J. Wiley & Sons, New York, 1987.
5. J. FREHSE, J. MÁLEK and M. STEINHAUER, An existence result for fluids with shear dependent viscosity-steady flows, Nonlin. Anal. Theory, Meth. & Appl. 30 (1997), 3041-3049.
6. J. FREHSE, J. MÁLEK and M. STEINHAUER, On analysis of steady flows of fluids with shear-dependent viscosity based on the Lipschitz truncation method, SIAM J. Math. Anal. 34 (2003), 1064-1083.
7. M. FUCHS, On quasi-static non-Newtonian fluids with power law, Math. Meth. Appl. Sciences 19 (1996), 1225-1231.
8. M. FUCHS and G. SEREGIN, Variational methods for problems from plasticity theory and for generalized Newtonian fluids, Lecture Notes Math. 1749, Springer, Berlin, 2000.
9. G. P. GALDI, An introduction to the mathematical theory of the Navier-Stokes equations, Vol. I: Linearized steady problems, Springer-Verlag, New York, 1994.
10. 1,α-solutions to a class of nonlinear fluids in two dimensions - stationary Dirichlet problem, Zap. Nauchn. Sem. St. Petersburg Otdel. Mat. Inst. Steklov (POMI) 259 (1999), 89-121.
11. H. LAMB, Hydrodynamics, 6th ed., Cambridge Univ. Press, Cambridge, 1945.
12. J. NAUMANN, On the differentiability of weak solutions of a degenerate system of PDE's in fluid mechanics, Annali Mat. pura appl. (IV) 151 (1988), 225-238.
13. J. NAUMANN and J. WOLF, On the interior regularity of weak solutions of degenerate elliptic systems (the case 1 < p < 2), Rend. Sem. Mat. Univ. Padova 68 (1992), 55-81.
14. M. RŮŽIČKA, A note on steady flow of fluids with shear dependent viscosity, Nonlin. Anal. Theory, Meth. & Appl. 30 (1997), 3029-3039.
15. W. L. WILKINSON, Non-Newtonian fluids. Fluid mechanics, mixing and heat transfer, Pergamon Press, London, New York, 1960.
16. 1,α-regularity of weak solutions to the equations of stationary motion to certain non-Newtonian fluids in two dimensions (to appear).