Hiroshima Mathematical Journal

A mixed formulation of the Stokes equations with slip conditions in exterior domains and in the half-space

Nabil Kerdid

Full-text: Open access

Abstract

We are concerned with Stokes equations in the half-space or in an exterior domain of $\mathbb{R}^n$ when slip conditions are imposed on the boundary. We present a mixed velocity-pressure formulation and we show its well posedness. A weighted variant of Korn’s inequality in unbounded domains is the cornerstone of our approach.

Article information

Source
Hiroshima Math. J., Volume 48, Number 2 (2018), 119-131.

Dates
Received: 4 January 2016
Revised: 9 March 2017
First available in Project Euclid: 1 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1533088823

Digital Object Identifier
doi:10.32917/hmj/1533088823

Mathematical Reviews number (MathSciNet)
MR3835552

Zentralblatt MATH identifier
06965536

Subjects
Primary: 76D07: Stokes and related (Oseen, etc.) flows 35E20: General theory 35Q35: PDEs in connection with fluid mechanics 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]

Keywords
Stokes equations unbounded domains exterior domain half-space weighted spaces Korn’s inequality

Citation

Kerdid, Nabil. A mixed formulation of the Stokes equations with slip conditions in exterior domains and in the half-space. Hiroshima Math. J. 48 (2018), no. 2, 119--131. doi:10.32917/hmj/1533088823. https://projecteuclid.org/euclid.hmj/1533088823


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