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The initial boundary value problem for Navier-Stokes equations

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Abstract

By making full use of the estimates of solutions to nonstationary Stokes equations and the method discussing global stability, we establish the global existence theorem of strong solutions for Navier-Stokes equatios in arbitrary three dimensional domain with uniformlyC 3 boundary, under the assumption that |a| L 2(Θ) + |f| L 1(0,∞;L 2(Θ)) or |∇a| L 2(Θ) + |f| L 2(0,∞;L 2(Θ)) small or viscosityv large. Herea is a given initial velocity andf is the external force. This improves on the previous results. Moreover, the solvability of the case with nonhomogeneous boundary conditions is also discussed.

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  1. Institute of Applied Mathmatics, Academia Sinica, 100080, Beijing, P. R. China

    Cheng He

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  1. Cheng He
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This work is supported by foundation of Institute of Mathematics, Academia Sinica

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He, C. The initial boundary value problem for Navier-Stokes equations. Acta Mathematica Sinica 15, 153–164 (1999). https://doi.org/10.1007/BF02650658

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  • DOI: https://doi.org/10.1007/BF02650658

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