Generalized Darcy-Oseen resolvent problem

Dagmar Medková; Mariya Ptashnyk; Werner Varnhorn

doi:10.1002/mma.3872

Generalized Darcy-Oseen resolvent problem

Dagmar Medková, Mariya Ptashnyk^*, Werner Varnhorn

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study the well-posedness of a coupled Darcy-Oseen resolvent problem, describing the fluid flow between free-fluid domains and porous media separated by a semipermeable membrane. The influence of osmotic effects, induced by the presence of a semipermeable membrane, on the flow velocity is reflected in the transmission conditions on the surface between the free-fluid domain and the porous medium. To prove the existence of a weak solution of the generalized Darcy-Oseen resolvent system, we consider two auxiliary problems: a mixed Navier-Dirichlet problem for the generalized Oseen resolvent system and Robin problem for an elliptic equation related to the general Darcy equations.

Original language	English
Pages (from-to)	1621-1630
Number of pages	10
Journal	Mathematical Methods in the Applied Sciences
Volume	39
Issue number	6
DOIs	https://doi.org/10.1002/mma.3872
Publication status	Published - Apr 2016

Keywords

Brinkman-Darcy equations
compact perturbations
Darcy-Oseen resolvent problem
fluid flow between free-fluid domains and porous media
semipermeable membrane

ASJC Scopus subject areas

General Mathematics
General Engineering

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10.1002/mma.3872Licence: CC BY

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title = "Generalized Darcy-Oseen resolvent problem",

abstract = "In this paper, we study the well-posedness of a coupled Darcy-Oseen resolvent problem, describing the fluid flow between free-fluid domains and porous media separated by a semipermeable membrane. The influence of osmotic effects, induced by the presence of a semipermeable membrane, on the flow velocity is reflected in the transmission conditions on the surface between the free-fluid domain and the porous medium. To prove the existence of a weak solution of the generalized Darcy-Oseen resolvent system, we consider two auxiliary problems: a mixed Navier-Dirichlet problem for the generalized Oseen resolvent system and Robin problem for an elliptic equation related to the general Darcy equations.",

keywords = "Brinkman-Darcy equations, compact perturbations, Darcy-Oseen resolvent problem, fluid flow between free-fluid domains and porous media, semipermeable membrane",

author = "Dagmar Medkov{\'a} and Mariya Ptashnyk and Werner Varnhorn",

note = "Funding Information: The research of D. M. was supported by RVO: 67985840. The research of M. P. was supported by EPSRC First Grant EP/K036521/1. Publisher Copyright: {\textcopyright} 2016 The Authors Mathematical Methods in the Applied Sciences Published by John Wiley & Sons Ltd.",

year = "2016",

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doi = "10.1002/mma.3872",

language = "English",

volume = "39",

pages = "1621--1630",

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T1 - Generalized Darcy-Oseen resolvent problem

AU - Medková, Dagmar

AU - Ptashnyk, Mariya

AU - Varnhorn, Werner

N1 - Funding Information: The research of D. M. was supported by RVO: 67985840. The research of M. P. was supported by EPSRC First Grant EP/K036521/1. Publisher Copyright: © 2016 The Authors Mathematical Methods in the Applied Sciences Published by John Wiley & Sons Ltd.

PY - 2016/4

Y1 - 2016/4

N2 - In this paper, we study the well-posedness of a coupled Darcy-Oseen resolvent problem, describing the fluid flow between free-fluid domains and porous media separated by a semipermeable membrane. The influence of osmotic effects, induced by the presence of a semipermeable membrane, on the flow velocity is reflected in the transmission conditions on the surface between the free-fluid domain and the porous medium. To prove the existence of a weak solution of the generalized Darcy-Oseen resolvent system, we consider two auxiliary problems: a mixed Navier-Dirichlet problem for the generalized Oseen resolvent system and Robin problem for an elliptic equation related to the general Darcy equations.

AB - In this paper, we study the well-posedness of a coupled Darcy-Oseen resolvent problem, describing the fluid flow between free-fluid domains and porous media separated by a semipermeable membrane. The influence of osmotic effects, induced by the presence of a semipermeable membrane, on the flow velocity is reflected in the transmission conditions on the surface between the free-fluid domain and the porous medium. To prove the existence of a weak solution of the generalized Darcy-Oseen resolvent system, we consider two auxiliary problems: a mixed Navier-Dirichlet problem for the generalized Oseen resolvent system and Robin problem for an elliptic equation related to the general Darcy equations.

KW - Brinkman-Darcy equations

KW - compact perturbations

KW - Darcy-Oseen resolvent problem

KW - fluid flow between free-fluid domains and porous media

KW - semipermeable membrane

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EP - 1630

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 6

ER -

Generalized Darcy-Oseen resolvent problem

Abstract

Keywords

ASJC Scopus subject areas

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