Acta Mathematica Sinica

, Volume 4, Issue 3, pp 210-226

First online:

Viscosity splitting method for three dimensional Navier-Stokes equations

  • Ying LunganAffiliated withDepartment of Mathematics, Peking University

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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 theH s+1 norm, 0≦s<3/2, of the approximate solutions and the order of theL 2 norm of the errors is obtained.