Electron. J. Diff. Equ., Vol. 2014 (2014), No. 250, pp. 1-9.

Navier-Stokes problem in velocity-pressure formulation: Newton linearization and convergence

Anis Younes, Abdennaceur Jarray, Mohamed Bouchiba

Abstract:
In this article we study the nonlinear Navier-Stokes problem in velocity-pressure formulation. We construct a sequence of a Newton-linearized problems and we show that the sequence of weak solutions converges towards the solution of the nonlinear one in a quadratic way.

Submitted January 3, 2013. Published December 1, 2014.
Math Subject Classifications: 35J20, 49J96.
Key Words: Navier-Stokes equations; Newton's algorithm; convergence.

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Anis Younes
Tunis El Manar University
Faculty of Sciences of Tunis, Tunisia
email: younesanis@yahoo.fr
Abdennaceur Jarray
Tunis El Manar University
Faculty of Sciences of Tunis, Tunisia
email: abdennaceur.jarray@gmail.com
Mohamed Bouchiba
Carthage University
National Institute of Applied Sciences and Technology
Tunisia
email: mohamed.bouchiba@yahoo.fr

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