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April, 2020 A Poisson Problem of Transmission-type for the Stokes and Generalized Brinkman Systems in Complementary Lipschitz Domains in $\mathbb{R}^3$
Andrei-Florin Albişoru
Taiwanese J. Math. 24(2): 331-354 (April, 2020). DOI: 10.11650/tjm/190408

Abstract

The purpose of this paper is to give a well-posedness result for a boundary value problem of transmission type for the Stokes and generalized Brinkman systems in two complementary Lipschitz domains in $\mathbb{R}^3$. In the first part of the paper, we have introduced the classical and weighted $L^2$-based Sobolev spaces on Lipschitz domains in $\mathbb{R}^3$. Afterwards, the trace and conormal derivative operators are defined in the case of both Stokes and generalized Brinkman systems. Also, a summary of the main properties of the layer potential operators for the Stokes system, is provided. In the second part of the work, we exploit the well-posedness of another transmission problem concerning the Stokes system on two complementary Lipschitz domains in $\mathbb{R}^3$ which is based on the Potential Theory for the Stokes system. Then, certain properties of Fredholm operators will allow us to show our main well-posedness result in $L^2$-based Sobolev spaces.

Citation

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Andrei-Florin Albişoru. "A Poisson Problem of Transmission-type for the Stokes and Generalized Brinkman Systems in Complementary Lipschitz Domains in $\mathbb{R}^3$." Taiwanese J. Math. 24 (2) 331 - 354, April, 2020. https://doi.org/10.11650/tjm/190408

Information

Received: 3 June 2018; Revised: 17 April 2019; Accepted: 23 April 2019; Published: April, 2020
First available in Project Euclid: 14 May 2019

zbMATH: 07192938
MathSciNet: MR4078201
Digital Object Identifier: 10.11650/tjm/190408

Subjects:
Primary: 35J25, 35Q35, 46E35

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

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Vol.24 • No. 2 • April, 2020
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