Differential and Integral Equations

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

Cătălin Popa

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

Export citation