Viscous splitting for the unbounded problem of the Navier-Stokes equations

Ying, Lung-An

doi:10.1090/S0025-5718-1990-1023053-0

Viscous splitting for the unbounded problem of the Navier-Stokes equations
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Math. Comp. 55 (1990), 89-113 Request permission

Abstract:

The viscous splitting for the exterior initial-boundary value problems of the Navier-Stokes equations is considered. It is proved that the approximate solutions are uniformly bounded in the space ${L^\infty }(0,T;{H^{s + 1}}(\Omega ))$, $s < \frac {3}{2}$, and converge with a rate of $O(k)$ in the space ${L^\infty }(0,T;{H^1}(\Omega ))$, where k is the length of the time steps.

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The viscosity splitting method for the Navier-Stokes equations in bounded domains

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