A weak-LpProdi-Serrin type regularity criterion for a bioconvective flow

Loayza, Miguel; Rojas-Medar, M.Drina; Rojas-Medar, Marko Antonio

doi:10.1080/00036811.2018.1451643

Cited by 1 publication

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References 13 publications

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“…The system (1)-( 6) was derived by Y. Moribe [2] and independently by M. Levandowsky, W. S. Hunter, and E. A. Spiegel [3] (see also [1,4,5] for the mathematical analysis). More recently, some new bioconvective flow models have been introduced, for instance: [6] (see also [7]) considered a generalized model with a nonconstant viscosity and the symmetric part of the deformation rate tensor, and Tuval et al [8] constructed a mathematical model by considering as an additional unknown variable: the oxygen concentration (see also [9][10][11]).…”

Section: Introductionmentioning

confidence: 99%

New Necessary Conditions for the Well-Posedness of Steady Bioconvective Flows and Their Small Perturbations

Coronel

Huancas

Tello

et al. 2021

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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.

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