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Équation anisotrope de Navier-Stokes dans des espaces critiques.

Marius Paicu (2005)

Revista Matemática Iberoamericana

We study the tridimensional Navier-Stokes equation when the value of the vertical viscosity is zero, in a critical space (invariant by the scaling). We shall prove local in time existence of the solution, respectively global in time when the initial data is small compared with the horizontal viscosity.

The Eulerian limit and the slip boundary conditions-admissible irregularity of the boundary

Piotr Bogusław Mucha (2005)

Banach Center Publications

We investigate the inviscid limit for the stationary Navier-Stokes equations in a two dimensional bounded domain with slip boundary conditions admitting nontrivial inflow across the boundary. We analyze admissible regularity of the boundary necessary to obtain convergence to a solution of the Euler system. The main result says that the boundary of the domain must be at least C²-piecewise smooth with possible interior angles between regular components less than π.

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