On the regularity of shear thickening viscous fluids

Chinese Annals of Mathematics. Series B

Volumn 30, Issue 3, 2009, Pages 273-280

  Crispo, Francesca ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

Boundary regularity; Non Newtonian fluids; Shear dependent viscosity

Indexed keywords

EID: 67349112853     PISSN: 02529599     EISSN: 18606261     Source Type: Journal    
DOI: 10.1007/s11401-007-0539-7     Document Type: Article

References (20)

1. E. Acerbi N. Fusco 1994 Partial regularity under anisotropic (p, q) growth conditions J. Diff. Eqs. 107 1 46 67
2. Astarita, G. and Marucci, G., Principles of Non-Newtonian Fluid Mechanics, McGraw-Hill, London, 1974.
3. H. Beirão da Veiga 2005 On the regularity of flows with Ladyzhenskaya shear dependent viscosity and slip or non-slip boundary conditions Comm. Pure Appl. Math. 58 552 577 (Pubitemid 40406005)
4. Beirão da Veiga, H., Navier-Stokes equations with shear thickening viscosity, regularity up to the boundary, J. Math. Fluid Mech. DOI: 10.1007/s00021-008-0257-2
5. Beirão da Veiga, H., Navier-Stokes equations with shear thinning viscosity, regularity up to the boundary, J. Math. Fluid Mech. DOI: 10.1007/s00021-008-0258-1
6. H. Beirão da Veiga 2009 On the Ladyzhenskaya-Smagorinsky turbulence model of the Navier-Stokes equations in smooth domains, the regularity problem J. Eur. Math. Soc. 11 127 167
7. H. Beirão da Veiga 2007 Concerning the Ladyzhenskaya-Smagorinsky turbulence model of the Navier-Stokes equations CR Acad. Sci. Paris 345 1 249 252
8. H. Beirão da Veiga 2009 On the global regularity of shear-thinning flows in smooth domains J. Math. Anal. Appl. 349 335 360
9. 2,q -regularity of incompressible fluids with shear-dependent viscosities: The shear thinning case, J. Math. Fluid Mech. DOI: 10.1007/s00021-008-0254-5
10. F. Crispo 2008 Shear thinning viscous fluids in cylindrical domains. Regularity up to the boundary J. Math. Flui Mech. 10 311 325
11. F. Crispo 2008 Global regularity of a class of p-fluid flows in cylinders J. Math. Anal. Appl. 341 559 574
12. Fuchs, M. and Seregin G., Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids, Lecture Notes in Mathematics, 1749, Springer-Verlag, Berlin, 2000.
13. Galdi, G. P., Mathematical problems in classical and non-Newtonian fluid mechanics, Hemodynamical Flows: Modeling, Analysis and Simulation (Oberwolfach Seminars), G. P. Galdi, A. M. Robertson, R. Rannacher, et al (eds.), Birkhaeuser-Verlag, Basel, 2007.
14. Lions, J. L., Quelques Méthodes de Résolution des Problèmes aux Limites Non-linéaires, Dunod and Gauthier-Villars, Paris, 1969.
15. Málek, J., Nečas, J., Rokyta, M. and Růž ička, M., Weak and measure-valued solutions to evolutionary PDEs, Applied Mathematics and Mathematical Computation, 13, Chapman and Hall, London, 1996.
16. J. Málek J. Nečas M. Růžička 1993 On the Non-Newtonian Incompressible Fluids Math. Models Methods Appl. Sci. 3 35 63
17. Nečas, J., équations aux Dérivées Partielles, Presses de l'Université de Montréal, Montréal, 1965.
18. C. Parés 1992 Existence, uniqueness and regularity of solution of the equations of a turbulence model for incompressible fluids Appl. Anal. 43 3-4 245 296
19. Rajagopal, K. R., Mechanics of non-newtonian fluids, Recent Developments in Theoretical FluidMechanics, G. P. Galdi and J. Nečas (eds.), Pitman Research Notes in Mathematics Series, 291, Longman, 1993, 129-162.
20. M. Troisi 1969 Teoremi di inclusione per spazi di Sobolev non isotropi Ricerche Mat. 18 3 24