Vol. 93, No. 2, 1981

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A uniqueness theorem for Navier-Stokes equations

Chun Ming Ma

Vol. 93 (1981), No. 2, 387–405

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
Received: 8 June 1979
Published: 1 April 1981
Chun Ming Ma