Differential and Integral Equations
- Differential Integral Equations
- Volume 15, Number 6 (2002), 657-670.
On the convergence of Euler-Stokes splitting of the Navier-Stokes equations
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.
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