On steady non-Newtonian fluids with growth conditions in generalized Orlicz spaces

Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda

DOI: http://dx.doi.org/10.12775/TMNA.2008.038

Abstract


We are interested in the existence of weak solutions to steady
non-Newtonian
fluids with nonstandard growth conditions of the Cauchy stress tensor.
Since the $L^p$ framework is not suitable to capture the description
of strongly inhomogeneous fluids, we formulate the problem in generalized
Orlicz spaces.
The existence proof consists in showing that for Galerkin approximations
the sequence of symmetric gradients of the flow velocity
converges modularly.
As an example of motivation for
considering non-Newtonian fluids in generalized Orlicz spaces we
recall the smart fluids.

Keywords


Non-Newtonian flows; Orlicz spaces; modular convergence; Young measures

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