A DISPERSIVE APPROACH TO THE ARTIFICIAL COMPRESSIBILITY APPROXIMATIONS OF THE NAVIER–STOKES EQUATIONS IN 3D
2006 ◽
Vol 03
(03)
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pp. 575-588
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Keyword(s):
In this paper we study how to approximate the Leray weak solutions of the incompressible Navier–Stokes equations. In particular we describe an hyperbolic version of the so-called artificial compressibility method investigated by J. L. Lions and Temam. By exploiting the wave equation structure of the pressure of the approximating system we achieve the convergence of the approximating sequences by means of dispersive estimates of Strichartz type. We prove that the projection of the approximating velocity fields on the divergence free vectors is relatively compact and converges to a Leray weak solution of the incompressible Navier–Stokes equation.
2017 ◽
Vol 20
(01)
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pp. 1650064
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1999 ◽
Vol 129
(5)
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pp. 903-912
2010 ◽
Vol 2010
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pp. 1-24
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2011 ◽
Vol 08
(01)
◽
pp. 101-113
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2010 ◽
Vol 229
(5)
◽
pp. 1698-1723
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