Abstract
<abstract><p>In this paper, we consider the first boundary value problem for a class of steady non-Newtonian micropolar fluid equations with heat convection in the three-dimensional smooth and bounded domain $ \Omega $. By using the fixed-point theorem and introducing a family of penalized problems, under the condition that the external force term and the vortex viscosity coefficient are appropriately small, the existence and uniqueness of strong solutions of the problem are obtained.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference31 articles.
1. G. Łukaszewicz, Micropolar Fluids: Theory and Applications, Springer Science & Business Media, 1999. https://doi.org/10.1017/s0022112099236889
2. W. R. Schowalter, Mechanics of Non-Newtonian Fluids, Pergamon Press: New York, 1978.
3. C. Truesdell, K. R. Rajagopal, An Introduction to the Mechanics of Fluids, Birkhauser: Basel, 2000. https://doi.org/10.1007/978-0-8176-4846-6
4. L. Brandolese, M. E. Schonbek, Large time decay and growth for solutions of a viscous Boussinesq system, Trans. Am. Math. Soc., 364 (2012), 5057–5090. https://doi.org/10.1090/S0002-9947-2012-05432-8
5. D. Chae, Global regularity for the 2D Boussinesq equations with partial viscosity terms, Adv. Math., 203 (2006), 497–513. https://doi.org/10.1016/j.aim.2005.05.001