TY  - JOUR
ID  - ncmm-2007-032
T1  - On uniqueness and time regularity of flows of power-law like non-Newtonian fluids
A1  - Bulíček, Miroslav
A1  - Ettwein, Frank
A1  - Kaplický, Petr
A1  - Pražák, Dalibor
JA  - Mathematical Methods in the Applied Sciences
Y1  - 2010
VL  - 33
IS  - 16
SP  - 1995
EP  - 2010
N1  - NCMM Preprint no. 2007-032
UR  - http://www.karlin.mff.cuni.cz/ncmm/preprints/07339180109article.pdf
M2  - doi: 10.1002/mma.1314
KW  - exponential attractor
KW  - non-Newtonian fluids
KW  - time regularity
KW  - uniqueness
N2  - Large class of non-Newtonian fluids can be characterized by index p, which gives the growth of the constitutively determined part of the Cauchy stress tensor. In this paper, the uniqueness and the time regularity of flows of these fluids in an open bounded three-dimensional domain is established for subcritical ps, i.e. for p>11/5. Our method works for ‘all’ physically relevant boundary conditions, the Cauchy stress need not be potential and it may depend explicitly on spatial and time variable. As a simple consequence of time regularity, pressure can be introduced as an integrable function even for Dirichlet boundary conditions.

Moreover, these results allow us to define a dynamical system corresponding to the problem and to establish the existence of an exponential attractor.
ER  -