Amru Hussein

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20182020

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math.AP2019

Primitive Equations with Horizontal Viscosity: The Initial Value and the Time-Periodic Problem for Physical Boundary Conditions

Amru Hussein, Martin Saal, Marc Wrona

The 3D-primitive equations with only horizontal viscosity are considered on a cylindrical domain $Ω = (- h, h) \times G$ , $G \subset R^{2}$ smooth, with the physical Dirichlet bo…

math.AP2018

Partial and full hyper-viscosity for Navier-Stokes and primitive equations

Amru Hussein

The $3$ -D primitive equations and incompressible Navier-Stokes equations with full hyper-viscosity and only horizontal hyper-viscosity are considered on the torus, i.e., the diffus…

math.AP2018

Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier-Stokes equations

Ken Furukawa, Yoshikazu Giga, Matthias Hieber +3

Consider the anisotropic Navier-Stokes equations as well as the primitive equations. It is shown that the horizontal velocity of the solution to the anisotropic Navier-Stokes equat…

math.AP2018

The Hydrostatic Stokes Semigroup and Well-Posedness of the Primitive Equations on Spaces of Bounded Functions

Yoshikazu Giga, Mathis Gries, Matthias Hieber +2

Consider the $3$ -d primitive equations in a layer domain $Ω = G \times (- h, 0)$ , $G = (0, 1)^{2}$ , subject to mixed Dirichlet and Neumann boundary conditions at $z = - h$ and $z = 0$ , respectiv…