Weak and classical solutions of equations of motion for third grade fluids

Jean-Marie Bernard

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 6, page 1091-1120
  • ISSN: 0764-583X

How to cite

top

Bernard, 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. [1] C. Amrouche, Etude Globale des Fluides de Troisième Grade. Thèse de 3e cycle,Université Pierre et Marie Curie, France (1986). 
  2. [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. [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. [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. [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. [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. [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. [8] E. A. Coddington and N. Levmson, Theory of Ordinary Differential Equations. Mc Graw-Hill, New York (1955). Zbl0064.33002MR69338
  9. [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. [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. [11] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris (1969). Zbl0189.40603MR259693
  12. [12] J. Nečas, Les méthodes directes en théorie des équations elliptiques. Masson, Paris (1967). MR227584
  13. [13] W. Noll and C. Truesdell, The Nonlinear Field Theory of Mechanics Handbuch of Physik, Vol. III. Springer-Verlag, Berlin(1975). Zbl0779.73004
  14. [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. [15] R. Temam, Navier-Stokes Equations. North-Holland, Amsterdam (1977). Zbl0383.35057
  16. [16] J. H. Videman, Mathematical analysis of viscoelastic non-Newtonzan fluids Thesis, University of Lisbonne (1997). 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.