Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
shear-dependent viscosity; incompressible fluid; global-in-time existence; weak solution
shear-dependent viscosity; incompressible fluid; global-in-time existence; weak solution
Summary:
We consider the two-dimesional spatially periodic problem for an evolutionary system describing unsteady motions of the fluid with shear-dependent viscosity under general assumptions on the form of nonlinear stress tensors that includes those with $p$-structure. The global-in-time existence of a weak solution is established. Some models where the nonlinear operator corresponds to the case $p=1$ are covered by this analysis.
References:
[1] Frehse, J., Málek, J., Steinhauer, M.: On existence results for fluids with shear dependent viscosity-unsteady flows. Partial Differential Equations, Theory and Numerical Solution, CRC Reserach Notes in Mathematics series, Vol. 406, W. Jäger, O. John, K. Najzar, J. Nečas, J. Stará (eds.), CRC Press UK, Boca Raton, 1999, pp. 121–129. MR 1713880
[2] Kaplický, P., Málek, J., Stará, J.: Global-in-time Hölder continuity of the velocity gradients for fluids with shear-dependent viscosities. Nonlinear Differ. Equ. Appl., submitted.
[3] Ladyzhenskaya, O. A.: On some new equations describing dynamics of incompressible fluids and on global solvability of boundary value problems to these equations. Trudy Math. Inst. Steklov. 102 (1967), 85–104.
[4] Lions, J.-L.: Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod, Paris, 1969. MR 0259693 | Zbl 0189.40603
[5] Lions, P.-L.: Mathematical Topics in Fluid Mechanics, Volume 1 (Incompressible Models). Oxford Lecture Series in Mathematics and its Applications 3, Oxford Science Publications, Clarendon Press, Oxford, 1996. MR 1422251
[1] Málek, J., Nečas, J., Rokyta, M., Růžička, M.: Weak and Measure-Valued Solutions to Evolutionary PDEs. Applied Mathematics and Mathematical Computation 13, Chapman & Hall, London, 1996. MR 1409366
Search
Partner of
