Artículo Original
Publicado 2009-03-05
Palabras clave
- Reproductive solution,
- two-grade fluid,
- Galerkin method
Cómo citar
Friz, L., Guillén-González, F., & Rojas-Medar, M. A. (2009). Reproductive solution for grade-two fluid model in two dimensions. Revista Integración, Temas De matemáticas, 27(1), 15–24. Recuperado a partir de https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/483
Resumen
We treat the existence of reproductive solution (weak periodic solution) of a second-grade fluid system in two dimensions, by using the Galerkin approximation method and compactness arguments.
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Referencias
[1] Cioranescu D. and El Hacène O. “Existence and uniqueness for fluids of second grade”, Nonlinear Partial Differential Equations and Their Applications, 109 (1984), 178–197. Collège de France Seminar, Pitman.
[2] Cioranescu D. and Girault V. “Weak and classical solutions of a family of second grade fluids”, Int. J. Non-Linear Mechanics, 32 (1997), 317–335.
[3] Climent-Ezquerra B., Guillén-González and Rojas-Medar M. “A review on reproductivity and time periodicity for incompressible fluids”, Bol. Soc. Esp. Mat. Apl. 41 (2007), 101–116.
[4] Dunn J. E. and Fosdick R. L. “Thermodynamics, stability and boundedness of fluids of complexity two and fluids of second grade”, Arch. Rat. Mech. Anal. 56 (1974),n 191–252.
[5] Fosdick R. L. and Rajapogal K. R. “Anomalous features in the model of second grade fluids”, Arch. Rat. Mech. Anal. 70 (1978), 145–152.
[6] Galdi G. P. and Sequeira A. “Further existence results for classical solutions of the equations of second-grade fluid”, Arch. Rat. Mech. Anal. 128 (1994), 297–312.
[7] Girault V. and Saadouni M. “On a time-dependent grade-two fluid in two dimensions”, Computers and Mathematics with Applications. 53 (2007), 347–360.
[8] Rivlin R. S. and Ericksen J. L. “Stress-deformation relations for isotropic materials”, J. Rational Mech. Anal. 4 (1955), 323–425.
[9] Truesdell C. and Noll W. “The Nonlinear Field Theories of Mechanics”, Handbuch der Physik, III/3, Springer-Verlag, Heidelberg (1965).
[2] Cioranescu D. and Girault V. “Weak and classical solutions of a family of second grade fluids”, Int. J. Non-Linear Mechanics, 32 (1997), 317–335.
[3] Climent-Ezquerra B., Guillén-González and Rojas-Medar M. “A review on reproductivity and time periodicity for incompressible fluids”, Bol. Soc. Esp. Mat. Apl. 41 (2007), 101–116.
[4] Dunn J. E. and Fosdick R. L. “Thermodynamics, stability and boundedness of fluids of complexity two and fluids of second grade”, Arch. Rat. Mech. Anal. 56 (1974),n 191–252.
[5] Fosdick R. L. and Rajapogal K. R. “Anomalous features in the model of second grade fluids”, Arch. Rat. Mech. Anal. 70 (1978), 145–152.
[6] Galdi G. P. and Sequeira A. “Further existence results for classical solutions of the equations of second-grade fluid”, Arch. Rat. Mech. Anal. 128 (1994), 297–312.
[7] Girault V. and Saadouni M. “On a time-dependent grade-two fluid in two dimensions”, Computers and Mathematics with Applications. 53 (2007), 347–360.
[8] Rivlin R. S. and Ericksen J. L. “Stress-deformation relations for isotropic materials”, J. Rational Mech. Anal. 4 (1955), 323–425.
[9] Truesdell C. and Noll W. “The Nonlinear Field Theories of Mechanics”, Handbuch der Physik, III/3, Springer-Verlag, Heidelberg (1965).