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Viscosity splitting method for three dimensional Navier-Stokes equations. (English) Zbl 0673.35085
Summary: Three dimensional initial boundary value problem of the Navier-Stokes equation is considered. The equation is split in an Euler equation and a non-stationary Stokes equation within each time step. Unlike the conventional approach, we apply a non-homogeneous Stokes equation instead of homogeneous one. Under the hypothesis that the original problem possesses a smooth solution, the estimate of the $$H^{s+1}$$ norm, $$0\leq s<3/2$$, of the approximate solution and the order of the $$L^ 2$$ norm of the errors is obtained.

MSC:
 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids 35B35 Stability in context of PDEs 35B65 Smoothness and regularity of solutions to PDEs
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References:
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