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Existence and Uniqueness of the Weak Solutions for the Steady Incompressible Navier-Stokes Equations with Damping

Volume 12, Number 2 (2011), 57 - 72

Existence and Uniqueness of the Weak Solutions for the Steady Incompressible Navier-Stokes Equations with Damping

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Abstract

This paper is concerned with the boundary-value problem for the steady incompressible Navier-Stokes equations with damping. Two cases are considered here: 1) the Dirichlet's boundary condition; 2) the nonhomogeneous boundary condition. we obtain the existence and uniqueness of the weak solutions for the steady incompressible Navier-Stokes equations with damping using different methods for the above cases.