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Viscosity splitting method for three dimensional Navier-Stokes equations

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Peking University, Beijing, China

    Ying Lungan

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  1. Ying Lungan
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This work was supported by the Science Foundation of Academia Sinica under grant (84)-103.

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Lungan, Y. Viscosity splitting method for three dimensional Navier-Stokes equations. Acta Mathematica Sinica 4, 210–226 (1988). https://doi.org/10.1007/BF02560577

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  • DOI: https://doi.org/10.1007/BF02560577

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