On uniqueness and time regularity of flows of power-law like non-Newtonian fluids

• Published in: Mathematical methods in the applied sciences 2010-11, Vol.33 (16), p.1995-2010
• Main Authors: Bulíček, Miroslav, Ettwein, Frank, Kaplický, Petr, Pražák, Dalibor
• Format: Article
• Language: English
• Subjects: Boundary conditions; Computational fluid dynamics; Dirichlet problem; Dynamical systems; Exact sciences and technology; exponential attractor; Global analysis, analysis on manifolds; Mathematical analysis; Mathematics; Non Newtonian fluids; Ordinary differential equations; Regularity; Sciences and techniques of general use; time regularity; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Uniqueness
• ISSN: 0170-4214; 1099-1476; 1099-1476
• DOI: 10.1002/mma.1314

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. Copyright © 2010 John Wiley & Sons, Ltd.