Interior C 1 , α -Regularity of Weak Solutions to the Equations of Stationary Motions of Certain Non-Newtonian Fluids in Two Dimensions

Jorg Wolf

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 2, page 317-340
  • ISSN: 0392-4041

Abstract

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In the present work we prove the interior Hölder continuity of the gradient matrix of any weak solution of equations, which describes the motion of non-Newtonian fluid in two dimensions, restricting ourself to the shear thinning case 1 < q < 2 .

How to cite

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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 10-B.2 (2007): 317-340. <http://eudml.org/doc/290418>.

@article{Wolf2007,
abstract = {In the present work we prove the interior Hölder continuity of the gradient matrix of any weak solution of equations, which describes the motion of non-Newtonian fluid in two dimensions, restricting ourself to the shear thinning case $1 < q < 2$.},
author = {Wolf, Jorg},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {317-340},
publisher = {Unione Matematica Italiana},
title = {Interior $C^\{1,\alpha\}$-Regularity of Weak Solutions to the Equations of Stationary Motions of Certain Non-Newtonian Fluids in Two Dimensions},
url = {http://eudml.org/doc/290418},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Wolf, Jorg
TI - Interior $C^{1,\alpha}$-Regularity of Weak Solutions to the Equations of Stationary Motions of Certain Non-Newtonian Fluids in Two Dimensions
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/6//
PB - Unione Matematica Italiana
VL - 10-B
IS - 2
SP - 317
EP - 340
AB - In the present work we prove the interior Hölder continuity of the gradient matrix of any weak solution of equations, which describes the motion of non-Newtonian fluid in two dimensions, restricting ourself to the shear thinning case $1 < q < 2$.
LA - eng
UR - http://eudml.org/doc/290418
ER -

References

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  1. ADAMS, A, R.., Sobolev spaces. Academic Press, Boston1978. MR450957
  2. ASTARITA, G. - MARRUCCI, G.Principles of non-Newtonian fluid mechanics. Mc Graw-Hill, London, New York 1974. Zbl0316.73001
  3. BATCHELOR, G. K., An introduction to fluid mechanics. Cambridge Univ. Press, Cambridge1967. Zbl0152.44402MR1744638
  4. BIRD, R. B. - ARMSTRONG, R. C., HASSAGER, O.: Dynamics of polymer liquids. Vol. 1: Fluid mechanics. 2nd ed., J. Wiley and Sons, New York1987. MR830199
  5. GALDI, G. P., An introduction to the mathematical theory of the Navier-Stokes equations. Vol. I: Linearized steady problems. Springer-Verlag, New York1994. Zbl0949.35004MR1284205DOI10.1007/978-1-4612-5364-8
  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). Zbl0516.49003MR717034
  7. GIAQUINTA, M. - MODICA, G., Almost-everywhere regularity results for solutions of nonlinear elliptic systems. Manuscripta Math.28 (1979), 109-158. Zbl0411.35018MR535699DOI10.1007/BF01647969
  8. GEHRING, F. W., L p integrability of the partial derivatives of a quasi conformal mapping. Acta. Math.130 (1973), 265- 277. Zbl0258.30021MR402038DOI10.1007/BF02392268
  9. KAPLICKÝ, P. - MÁLEK, J. - STARÁ, J., C 1 , α -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. Zbl0978.35046MR1754359DOI10.1023/A:1014440207817
  10. LAMB, H., Hydrodynamics. 6th ed., Cambridge Univ. Press1945. MR1317348
  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. Zbl0664.35033MR964511DOI10.1007/BF01762796
  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. Padova88 (1992), 55- 81. Zbl0818.35024MR1209116
  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. Zbl1070.35023MR2177130DOI10.1007/s00021-004-0120-z
  14. WILKINSON, W. L., Non-Newtonian fluids. Fluid mechanics, mixing and heat transfer. Pergamon Press, London, New York1960. Zbl0124.41802MR110392

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