Wolf: Interior $C^{1,\alpha}$-Regularity of Weak Solutions to the Equations of Stationary Motions of Certain Non-Newtonian Fluids in Two Dimensions

Wolf, Jorg:
Interior $C^{1,\alpha}$-Regularity of Weak Solutions to the Equations of Stationary Motions of Certain Non-Newtonian Fluids in Two Dimensions
Bollettino dell'Unione Matematica Italiana Serie 8 10-B (2007), fasc. n.2, p. 317-340, Unione Matematica Italiana (English)
pdf (540 Kb), djvu (190 Kb). | MR 2339444 | Zbl 1140.76007

Sunto

Si dimostra l'hölderianità di equazioni degenerate, che descrivono il moto di un fluido incomprimibile non- newtoniano in due dimensioni, sotto condizioni usuali di monotonia e di andamento all'infinito di ordine $q - 1$ ($1 < q < 2$).

Referenze Bibliografiche

[1] ADAMS, R. A., Sobolev spaces. Academic Press, Boston 1978. | MR 450957

[2] ASTARITA, G. - MARRUCCI, G. Principles of non-Newtonian fluid mechanics. Mc Graw-Hill, London, New York 1974. | Zbl 0316.73001

[3] BATCHELOR, G. K., An introduction to fluid mechanics. Cambridge Univ. Press, Cambridge 1967. | MR 1744638 | Zbl 0152.44402

[4] BIRD, R. B. - ARMSTRONG, R. C., HASSAGER, O.: Dynamics of polymer liquids. Vol. 1: Fluid mechanics. 2nd ed., J. Wiley and Sons, New York 1987. | MR 830199

[5] GALDI, G. P., An introduction to the mathematical theory of the Navier-Stokes equations. Vol. I: Linearized steady problems. Springer-Verlag, New York 1994. | fulltext (doi) | MR 1284205 | Zbl 0949.35004

[6] GIAQUINTA, M., Multiple integrals in the calculus of variations and nonlinear elliptic systems. Annals Math. Studies, no. 105, Princeton Univ. Press, Princeton, N.J. (1983). | MR 717034 | Zbl 0516.49003

[7] GIAQUINTA, M. - MODICA, G., Almost-everywhere regularity results for solutions of nonlinear elliptic systems. Manuscripta Math. 28 (1979), 109-158. | fulltext EuDML | fulltext (doi) | MR 535699 | Zbl 0411.35018

[8] GEHRING, F. W., $L^p$integrability of the partial derivatives of a quasi conformal mapping. Acta. Math. 130 (1973), 265- 277. | fulltext (doi) | MR 402038 | Zbl 0258.30021

[9] KAPLICKÝ, P. - MÁLEK, J. - STARÁ, J., $C^{1, \alpha}$-solutions to a class of nonlinear fluids in two dimensionsÀstationary Dirichlet problem. Zap. Nauchn. Sem. St. Petersburg Odtel. Mat. Inst. Steklov (POMI) 259 (1999), 89-121. | fulltext (doi) | MR 1754359 | Zbl 0978.35046

[10] LAMB, H., Hydrodynamics. 6th ed., Cambridge Univ. Press 1945. | MR 1317348

[11] NAUMANN, J., 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. | fulltext (doi) | MR 964511 | Zbl 0664.35033

[12] NAUMANN, J. - WOLF, J., On the interior regularity of weak solutions of degenerate elliptic system (the case $1 < p < 2$). Rend. Sem. Mat. Univ. Padova 88 (1992), 55- 81. | fulltext EuDML | MR 1209116 | Zbl 0818.35024

[13] NAUMANN, J. - WOLF, J., Interior differentiability of weak solutions to the equations of stationary motion of a class of non-Newtonian fluids J. Math. Fluid Mech., 7 (2005), 298-313. | fulltext (doi) | MR 2177130 | Zbl 1070.35023

[14] WILKINSON, W. L., Non-Newtonian fluids. Fluid mechanics, mixing and heat transfer. Pergamon Press, London, New York 1960. | MR 110392 | Zbl 0124.41802

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Sunto

Referenze Bibliografiche