On strong solutions of the differential equations modeling the steady flow of certain incompressible generalized Newtonian fluids

Bildhauer, M.; Fuchs, M.; Zhong, X.

doi:10.1090/S1061-0022-07-00948-X

On strong solutions of the differential equations modeling the steady flow of certain incompressible generalized Newtonian fluids
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by M. Bildhauer, M. Fuchs and X. Zhong

St. Petersburg Math. J. 18 (2007), 183-199

DOI: https://doi.org/10.1090/S1061-0022-07-00948-X

Published electronically: March 16, 2007

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Abstract:

A system of nonautonomous partial differential equations describing the steady flow of an incompressible fluid is considered. The existence of a strong solution of that system is proved under suitable assumptions on the data. In the 2D-case this solution turns out to be of class $C^{1,\alpha }$.

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