Existence and uniqueness of global solutions for the modified anisotropic 3D Navier−Stokes equations

Hakima Bessaih, Saber Trabelsi, Hamdi Zorgati

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We study a modified three-dimensional incompressible anisotropic Navier−Stokes equations. The modification consists in the addition of a power term to the nonlinear convective one. This modification appears naturally in porous media when a fluid obeys the Darcy−Forchheimer law instead of the classical Darcy law. We prove global in time existence and uniqueness of solutions without assuming the smallness condition on the initial data. This improves the result obtained for the classical 3D incompressible anisotropic Navier−Stokes equations.
Original languageEnglish (US)
Pages (from-to)1817-1823
Number of pages7
JournalESAIM: Mathematical Modelling and Numerical Analysis
Issue number6
StatePublished - Oct 18 2016

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