A result on the existence and uniqueness of stationary solutions for a bioconvective flow model (original) (raw)
2017, arXiv (Cornell University)
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Axioms
We introduce new necessary conditions for the existence and uniqueness of stationary weak solutions and the existence of the weak solutions for the evolution problem in the system arising from the modeling of the bioconvective flow problem. Our analysis is based on the application of the Galerkin method, and the system considered consists of three equations: the nonlinear Navier–Stokes equation, the incompressibility equation, and a parabolic conservation equation, where the unknowns are the fluid velocity, the hydrostatic pressure, and the concentration of microorganisms. The boundary conditions are homogeneous and of zero-flux-type, for the cases of fluid velocity and microorganism concentration, respectively.
Time-reproductive solutions for a bioconvective flow
2013
We consider the existence and uniqueness of periodic solutions for the generalized bioconvective flow, which is a well known model to describe the convection caused by the concentration of upward swimming microorganism in a fluid.
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