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Penalty approximations to the stationary power-law Navier-Stokes problem. (English) Zbl 0997.76007

Summary: We study penalty approximations to steady-state Navier-Stokes problem governed by the power-law model for viscous incompressible non-Newtonian flows in bounded convex domains in \(\mathbb{R}^d\) \((2\leq d)\). Existence and uniqueness of solutions to the penalty approximations are proved, convergence is shown, and rates of convergence are estimated.

MSC:

76A05 Non-Newtonian fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35Q35 PDEs in connection with fluid mechanics
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