A note on the existence and uniqueness of plane steady viscous flow in exterior domains

Article type: Research Article

Authors: Tachim Medjo, T.

Affiliations: Department of Mathematics, Florida International University, DM413B University Park, Miami, FL 33199, USA E‐mail: [email protected]

Abstract: In this article we study the existence and uniqueness of solutions of the stationary Navier–Stokes equations in two‐dimensional exterior domains. Using well‐known Lq‐estimates for the Oseen problems and an iterative process based on repeated resolution of Oseen problems, we prove the existence and uniqueness of solutions of the Navier–Stokes equations in two‐dimensional exterior domains. Our results give another answer to a question recently raised in [2,3] concerning the summability with exponent p∈(1,2) of the gradient of the velocity of stationary plane flow of a viscous fluid in exterior domains.

Journal: Asymptotic Analysis, vol. 29, no. 3-4, pp. 283-291, 2002