Generalized Stokes system in Orlicz spaces

Piotr Gwiazda; Agnieszka Świerczewska-Gwiazda; Aneta Wróblewska

doi:10.3934/dcds.2012.32.2125

Article Contents

2012, Volume 32, Issue 6: 2125-2146. Doi: 10.3934/dcds.2012.32.2125

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Generalized Stokes system in Orlicz spaces

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

Received: January 2011

Revised: September 2011

Published: June 2012

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Abstract

The paper concerns the generalized Stokes system with the nonlinear term having growth conditions prescribed by an ${\mathcal{N}}-$function. Our main interest is directed to relaxing the assumptions on the ${\mathcal{N}}-$function and in particular to capture the shear thinning fluids with rheology close to linear. The case of anisotropic functions is considered. The existence of weak solutions is the main result of the present paper. Additionally, for the purpose of the existence proof, a version of the Sobolev-Korn inequality in Orlicz spaces is proved.

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Mathematics Subject Classification: 35K55, 35K30, 76D07.

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