Weak and classical solutions of equations of motion for third grade fluids
- Volume: 33, Issue: 6, page 1091-1120
- ISSN: 0764-583X
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topBernard, Jean-Marie. "Weak and classical solutions of equations of motion for third grade fluids." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.6 (1999): 1091-1120. <http://eudml.org/doc/193963>.
@article{Bernard1999,
author = {Bernard, Jean-Marie},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Galerkin method; special basis; decomposition method; weak solution; classical solution; third grade fluid; global existence of solution; small initial data; regularity; energy estimate},
language = {eng},
number = {6},
pages = {1091-1120},
publisher = {Dunod},
title = {Weak and classical solutions of equations of motion for third grade fluids},
url = {http://eudml.org/doc/193963},
volume = {33},
year = {1999},
}
TY - JOUR
AU - Bernard, Jean-Marie
TI - Weak and classical solutions of equations of motion for third grade fluids
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 6
SP - 1091
EP - 1120
LA - eng
KW - Galerkin method; special basis; decomposition method; weak solution; classical solution; third grade fluid; global existence of solution; small initial data; regularity; energy estimate
UR - http://eudml.org/doc/193963
ER -
References
top- [1] C. Amrouche, Etude Globale des Fluides de Troisième Grade. Thèse de 3e cycle,Université Pierre et Marie Curie, France (1986).
- [2] C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in Three-Dimensional Nonsmooth Domains. Math. Methods Appl. Sci. 21 (1998) 823-864. Zbl0914.35094MR1626990
- [3] C. Amrouche and D. Cioranescu, On a class of fluids of grade 3. Internat. J. Non-linear Mech. 32 (1997) 73-88. Zbl0887.76007MR1432717
- [4] D. Bresch and J. Lemome, On the Existence of Strong Solutions for Non-Stationary Third-Grade Fluids Preprint, Université Blaise Pascal, Clermont-Ferrand (1996).
- [5] D. Cioranescu and V. Girault, Weak and classical solutions of a family of second grade fluids. Internat J. Non-linear Mech. 32 (1997) 317-335. Zbl0891.76005MR1433927
- [6] D. Cioranescu and E. H. Ouazar, Existence et unicité pour les fluides de second grade. C. R. Acad. Sci. Sér. I 298 (1984) 285-287. Zbl0571.76005MR765424
- [7] D. Cioranescu and E. H. Ouazar, Existence and uniqueness for fluids of second grade, in Nonlinear Partial Differential Equations, Collège de France Seminar, Pitman, 109 (1984) 178-197. Zbl0577.76012MR772241
- [8] E. A. Coddington and N. Levmson, Theory of Ordinary Differential Equations. Mc Graw-Hill, New York (1955). Zbl0064.33002MR69338
- [9] R. L. Fosdick and K. R. Rajagopal, Thermodynamics and stability of fluids of third grade. Proc. Roy. Soc. London Ser. A 339(1980) 351-377. Zbl0441.76002MR559220
- [10] G. P. Galdi, M. Grobbelaar-Van Dalsen and N. Sauer, Existence and uniqueness of classical solutions of the equations of motion for second grade fluids. Arch. Rational Mech. Anal. VIA (1993) 221-237. Zbl0804.76003MR1237911
- [11] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris (1969). Zbl0189.40603MR259693
- [12] J. Nečas, Les méthodes directes en théorie des équations elliptiques. Masson, Paris (1967). MR227584
- [13] W. Noll and C. Truesdell, The Nonlinear Field Theory of Mechanics Handbuch of Physik, Vol. III. Springer-Verlag, Berlin(1975). Zbl0779.73004
- [14] A. Sequeira and J. Videman, Global existence of classical solutions for the equations of third grade fluids. J. Math. Phys. Sci.29 (1995) 47-69. Zbl0839.76005MR1369934
- [15] R. Temam, Navier-Stokes Equations. North-Holland, Amsterdam (1977). Zbl0383.35057
- [16] J. H. Videman, Mathematical analysis of viscoelastic non-Newtonzan fluids Thesis, University of Lisbonne (1997).
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