On the Leray problem and the Poiseuille flow

Article type: Research Article

Authors: Chipot, Michel^{; *}

Affiliations: Institute of Mathematics, University of Zürich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: The goal of this note is to present a simple proof of existence and uniqueness of the solution of the Leray problem for high viscosities and homogeneous or non homogeneous boundary conditions. Furthermore we address the issue of uniqueness of the Poiseuille flow in a pipe.

Keywords: Nonlinear elliptic equations, Navier Stokes, stationary problem, Poiseuille flow

DOI: 10.3233/ASY-211708

Journal: Asymptotic Analysis, vol. 128, no. 3, pp. 337-350, 2022