On the anisotropic Orlicz spaces applied in the problems of continuum mechanics

Piotr Gwiazda; Piotr Minakowski; Agnieszka Świerczewska-Gwiazda

doi:10.3934/dcdss.2013.6.1291

Article Contents

2013, Volume 6, Issue 5: 1291-1306. Doi: 10.3934/dcdss.2013.6.1291

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On the anisotropic Orlicz spaces applied in the problems of continuum mechanics

1.
Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa

Received: October 31, 2011

Published: September 2013

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Abstract

The paper concerns theory of anisotropic Orlicz spaces and its applications in continuum mechanics. Our main motivations are e.g. flow of non-Newtonian fluid and response of inelastic materials with non-standard growth conditions of the Cauchy stress tensor. The set of basic definitions and theorems with proofs is presented. We prove the existence of a weak solutions to the generalized Stokes system. Overview covering recent results in the referred topic is given.

Keywords:

Non-Newtonian fluids,
Orlicz spaces.

Mathematics Subject Classification: 35Q35, 46E30.

Citation:

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