Existence results for the flow of viscoelastic fluids with a differential constitutive law

Astarita, 1974

Bourguignon, 1976, Remarks on the Euler equation, J. Funct. Analysis, 15, 341, 10.1016/0022-1236(74)90027-5

Constantin, 1989

Crochet, 1984

Dupret, 1986, Sur le signe des valeurs propres du tenseur des extra-contraintes dans un écoulement de fluide de Maxwell, J. Méc. Théor. Applic., 5, 403

Dupret, 1985, On the consequence of discretization errors in the numerical calculation of viscoelastic flow, J. Non-Newtonian Fluid Mech., 18, 173, 10.1016/0377-0257(85)85020-5

Giesekus, 1982, A unified approach to a variety of constitutive models for polymer fluids based on the concept of configuration dependent molecular mobility, Rheol. Acta, 21, 366, 10.1007/BF01534296

Guillopé, 1987, Résultats d'existence pour des fluides viscoélastiques á loi de comportement de type différentiel, C.r. Acad. Sci. Paris, 305, 489

Guillopé, 1990, Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type, M2AN, 24, 369, 10.1051/m2an/1990240303691

Joseph, 1985, Hyperbolicity and change of type in the flow of viscoelastic fluid, Archs ration. Mech. Analysis, 81, 53

Joseph, 1986, Change of type and loss of evolution in the flow of viscoelastic fluids, J. Non-Newtonian Fluid Mech., 20, 117, 10.1016/0377-0257(86)80018-0

Larson, 1987, A critical comparison of constitutive equations for polymer melts, J. Non-Newtonian Fluid Mech., 23, 249, 10.1016/0377-0257(87)80021-6

Leonov, 1976, Nonequilibrium thermodynamics and rheology of viscoelastic polymer media, Rheol. Acta, 15, 85, 10.1007/BF01517499

Lions, 1969

Oldroyd, 1950, On the formation of rheological equations of state, Proc. R. Soc. Lond., A 200, 523, 10.1098/rspa.1950.0035

Phan-Thien, 1977, A new constitutive equation derived from network theory, J. Non-Newtonian Fluid Mech., 2, 353, 10.1016/0377-0257(77)80021-9

Renardy, 1985, Existence of slow steady flows of viscoelastic fluids with differential constitutive equations, Z. angew. Math. Mech., 65, 449, 10.1002/zamm.19850650919

Renardy, 1987

Serrin, 1959, A note on the existence of periodic solutions of the Navier-Stokes equations, Archs ration. Mech. Analysis, 3, 120, 10.1007/BF00284169

Temam, 1977

Valli, 1983, Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method, Annali Scu. norm. sup. Pisa, 10, 607

Valli, 1986, Navier-Stokes equations for compressible fluids: global estimates and periodic solutions, Proc. Symp. Pure Math., 45, 467, 10.1090/pspum/045.2/843633