A uniqueness theorem for Navier-Stokes equations

Chun Ming Ma

Vol. 93 (1981), No. 2, 387–405

DOI: 10.2140/pjm.1981.93.387

Abstract

In this paper we consider the initial boundary value problem for the Navier-Stokes equations in several types of unbounded three-dimensional domains Ω. We prove uniqueness within a class of solutions, which we call “weak class H₀ solutions”, whose members satisfy the integrability conditions ∇u, Δu ∈ L²(0,T;L₂(Ω)). Moreover, the solutions are shown to depend continuously on their initial values. The results are based, primarily on establishing a simple characterization of a certain space H₀(Ω) of solenoidal functions.

Mathematical Subject Classification 2000

Primary: 35Q10, 35Q10

Secondary: 76D05

Milestones

Received: 8 June 1979

Published: 1 April 1981