Differential and Integral Equations

On the convergence of Euler-Stokes splitting of the Navier-Stokes equations

Cătălin Popa

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Abstract

We consider Euler--Stokes splitting approximation of the Navier--Stokes equations with no--slip boundary condition. This consists in alternate solving of the Euler equations with tangential boundary condition and Stokes equations with no-slip boundary condition on small time intervals of the same length $k$. In a previous paper, J.T. Beale and C. Greengard proved the convergence of this approximation scheme in $L^p$ norm as $k$ tends to zero, for smooth solutions of the Navier--Stokes equations. Here we show how a certain simplification in their arguments improves their main result in the following way: the convergence holds without any additional regularity assumption on the solution of the Navier--Stokes equations.

Article information

Source
Differential Integral Equations, Volume 15, Number 6 (2002), 657-670.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060810

Mathematical Reviews number (MathSciNet)
MR1893840

Zentralblatt MATH identifier
1048.35067

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]
Secondary: 76D05: Navier-Stokes equations [See also 35Q30]

Citation

Popa, Cătălin. On the convergence of Euler-Stokes splitting of the Navier-Stokes equations. Differential Integral Equations 15 (2002), no. 6, 657--670. https://projecteuclid.org/euclid.die/1356060810


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