Remarks on Zero Viscosity Limit for Nonstationary Navier- Stokes Flows with Boundary

This paper is concerned with the question of convergence of the nonstationary, incompressible Navier-Stokes flow u = u v to the Euler flow u as the viscosity v tends to zero. If the underlying space domain is all of Rm, the convergence has been proved by several authors under appropriate assumptions on the convergence of the data (initial condition and external force); see Golovkin [1] and McGrath [2] for m = 2 and all time, and Swann [3] and the author [4,5] for m = 3 and short time. The case m ⩾ 4 can be handled in the same way; in fact, the simple method given in [5] applies to any dimension. All these results refer to strong solutions (or even classical solutions, depending on the data) of the Navier-Stokes equation.

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