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

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

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 me...

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Main Authors: Aníbal Coronel, Fernando Huancas, Alex Tello, Marko Rojas-Medar
Format: Article
Language:English
Published: MDPI AG 2021-08-01
Series:Axioms
Subjects:
bioconvective flow
Navier–Stokes system
Galerkin estimates
Online Access:https://www.mdpi.com/2075-1680/10/3/205
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spelling doaj-61f4f2d7f44b454b88ebab76cfbfb9c72021-09-25T23:44:55ZengMDPI AGAxioms2075-16802021-08-011020520510.3390/axioms10030205New Necessary Conditions for the Well-Posedness of Steady Bioconvective Flows and Their Small PerturbationsAníbal Coronel0Fernando Huancas1Alex Tello2Marko Rojas-Medar3Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán 3780000, ChileDepartamento de Matemática, Facultad de Ciencias Naturales, Matemáticas y del Medio Ambiente, Universidad Tecnológica Metropolitana, Las Palmeras 3360, Ñuñoa-Santiago 7750000, ChileDepartamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán 3780000, ChileDepartamento de Matemática, Universidad de Tarapacá, Casilla 7D, Arica 1000000, ChileWe 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.https://www.mdpi.com/2075-1680/10/3/205bioconvective flowNavier–Stokes systemGalerkin estimates
collection DOAJ
language English
format Article
sources DOAJ
author Aníbal Coronel
Fernando Huancas
Alex Tello
Marko Rojas-Medar
spellingShingle Aníbal Coronel
Fernando Huancas
Alex Tello
Marko Rojas-Medar
New Necessary Conditions for the Well-Posedness of Steady Bioconvective Flows and Their Small Perturbations
Axioms
bioconvective flow
Navier–Stokes system
Galerkin estimates
author_facet Aníbal Coronel
Fernando Huancas
Alex Tello
Marko Rojas-Medar
author_sort Aníbal Coronel
title New Necessary Conditions for the Well-Posedness of Steady Bioconvective Flows and Their Small Perturbations
title_short New Necessary Conditions for the Well-Posedness of Steady Bioconvective Flows and Their Small Perturbations
title_full New Necessary Conditions for the Well-Posedness of Steady Bioconvective Flows and Their Small Perturbations
title_fullStr New Necessary Conditions for the Well-Posedness of Steady Bioconvective Flows and Their Small Perturbations
title_full_unstemmed New Necessary Conditions for the Well-Posedness of Steady Bioconvective Flows and Their Small Perturbations
title_sort new necessary conditions for the well-posedness of steady bioconvective flows and their small perturbations
publisher MDPI AG
series Axioms
issn 2075-1680
publishDate 2021-08-01
description 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.
topic bioconvective flow
Navier–Stokes system
Galerkin estimates
url https://www.mdpi.com/2075-1680/10/3/205
work_keys_str_mv AT anibalcoronel newnecessaryconditionsforthewellposednessofsteadybioconvectiveflowsandtheirsmallperturbations
AT fernandohuancas newnecessaryconditionsforthewellposednessofsteadybioconvectiveflowsandtheirsmallperturbations
AT alextello newnecessaryconditionsforthewellposednessofsteadybioconvectiveflowsandtheirsmallperturbations
AT markorojasmedar newnecessaryconditionsforthewellposednessofsteadybioconvectiveflowsandtheirsmallperturbations
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