This is the first book to present a model, based on rational
mechanics of electrorheological fluids, that takes into account the
complex interactions between the electromagnetic fields and the
moving liquid. Several constitutive relations for the Cauchy stress
tensor are discussed. The main part of the book is devoted to a
mathematical investigation of a model possessing shear-dependent
viscosities, proving the existence and uniqueness of weak and
strong solutions for the steady and the unsteady case. The PDS
systems investigated possess so-called non-standard growth
conditions. Existence results for elliptic systems with
non-standard growth conditions and with a nontrivial nonlinear
r.h.s. and the first ever results for parabolic systems with a
non-standard growth conditions are given for the first time.
Written for advanced graduate students, as well as for researchers
in the field, the discussion of both the modeling and the
mathematics is self-contained.
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