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| We study a system of partial differential equations describing the steady
flow of a heat conducting incompressible fluid in a bounded three
dimensional domain, where the right-hand side of the momentum equation
includes the buoyancy force. In the present work we prove the existence
of a weak solution under both the smallness and a sign condition on
physical parameters $\alpha _0$ and $\alpha _1$ which appear on the right
hand side. The presentation is based on the paper: {\it On the existence of weak solutions to the equations of steady flow of heat-conducting fluids with dissipative heating}, Nonlinear Analysis, Series B: Real World Applications {\bf 13} (2012), No. 4, 1600--1620. |
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