Title page for ETD etd-06212011-120758


Document Type Doctoral Thesis
Author Razafimandimby, Paul Andre
Email paulrazafi@gmail.com
URN etd-06212011-120758
Document Title Some mathematical problems in the dynamics of stochastic second-grade fluids
Degree PhD
Department Mathematics and Applied Mathematics
Supervisor
Advisor Name Title
Prof M Sango Supervisor
Keywords
  • stochastic system
  • bidimensional second grade fluid
  • Lipschitz conditions
Date 2011-04-05
Availability unrestricted
Abstract
In the present work we initiate the investigation of a stochastic system of evolution partial differential equations modelling the turbulent flows of a bidimensional second grade fluid.

Global existence and uniqueness of strong probabilistic solution (but weak in the sense of partial differential equations) are expounded. We also give two results on the long time behavior of the strong probabilistic solution of this stochastic model. Mainly we prove that the strong probabilistic solution of our stochastic model converges exponentially in mean square to the stationary solution of the time-independent second grade fluids equations if the deterministic part of the external force does not depend on time. In the time-dependent case the strong probabilistic solution decays exponentially in mean square. These results are obtained under Lipschitz conditions on the forces entering in the model considered.

We also establish the global existence of weak probabilistic solution when the Lipschitz condition on the forces no longer holds.

Finally, we show that under suitable conditions on the data we can construct a sequence of strong probabilistic solutions of the stochastic second grade fluid that converges to the strong probabilistic solution of the stochastic Navier-Stokes equations when the stress modulus tends to zero.

All these results are new for the stochastic second-grade fluid and generalize the corresponding results obtained for the deterministic second-grade fluids.

2010 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.

Please cite as follows:

Razafimandimby, PA 2010, Some mathematical problems in the dynamics of stochastic second-grade fluids, PhD thesis, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-06212011-120758/ >

D11/377/ag

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