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On uniqueness and time regularity of flows of power-law like non-Newtonian fluids
Type of publication: Article
Citation: ncmm-2007-032
Journal: Mathematical Methods in the Applied Sciences
Volume: 33
Number: 16
Year: 2010
Pages: 1995-2010
Note: NCMM Preprint no. 2007-032
URL: http://www.karlin.mff.cuni.cz/...
DOI: 10.1002/mma.1314
Abstract: 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.
Keywords: exponential attractor, non-Newtonian fluids, time regularity, uniqueness
Authors Bulíček, Miroslav
Ettwein, Frank
Kaplický, Petr
Pražák, Dalibor
Added by: [JH]
Total mark: 0
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