Local pressure methods  in Orlicz spaces for the motion of rigid bodies in a non-Newtonian fluid with       general growth conditions

Aneta Wróblewska-Kamińska

doi:10.3934/dcdss.2013.6.1417

Article Contents

2013, Volume 6, Issue 5: 1417-1425. Doi: 10.3934/dcdss.2013.6.1417

This issue Previous Article Analytic rates of solutions to the Euler equations Next Article Long time existence of regular solutions to non-homogeneous Navier-Stokes equations

Local pressure methods in Orlicz spaces for the motion of rigid bodies in a non-Newtonian fluid with general growth conditions

Aneta Wróblewska-Kamińska^1,

1.
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa

Received: October 31, 2011

Revised: January 31, 2012

Published: September 2013

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Abstract

In the present paper we provide the decomposition and local estimates for the pressure function for the non-stationary flow of incompressible non-Newtonian fluids in Orlicz spaces. We show that this method can be applied to prove the existence of weak solutions to the problem of motion of one or several rigid bodies in a non-Newtonian incompressible fluid with growth conditions given by an $N$-function.

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Mathematics Subject Classification: Primary: 35Q35, 46E30, 76D03.

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