Electron. J. Diff. Equ., Vol. 2013 (2013), No. 110, pp. 1-15.

Existence and uniqueness of stationary solutions to bioconvective flow equations

Jose Luiz Boldrini, Marko Antonio Rojas-Medar, Maria Drina Rojas-Medar

We analyze a system of nonlinear partial differential equations modeling the stationary flow induced by the upward swimming of certain microorganisms in a fluid. We consider the realistic case in which the effective viscosity of the fluid depends on the concentration of such microorganisms. Under certain conditions, we prove the existence and uniqueness of solutions for such generalized bioconvective flow equations

Submitted January 17, 2013. Published April 29, 2013.
Math Subject Classifications: 35Q80, 76Z10, 92B05.
Key Words: Bioconvective flow; stationary solutions.

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José Luiz Boldrini
Unicamp-Imecc, Rua Sérgio Buarque de Holanda
651: 13083-859 Campinas, SP, Brazil
email: josephbold@gmail.com
Marko Antonio Rojas-Medar
Dpto. de Ciencias Básicas, Facultad de Ciencias
Universidad del Bío-Bío, Campus Fernando May
Casilla 447, Chillán, Chile
email: marko@ubiobio.cl
Maria Drina Rojas-Medar
Dpto. de Matemáticas, Facultad de Ciencias Básicas
Universidad de Antofagasta, Casilla 170
Antofagasta, Chile
email: mrojas@uantof.cl

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