The Initial Boundary Value Problem for Navier-Stokes Equations

Cheng He

Acta Mathematica Sinica ›› 1999, Vol. 15 ›› Issue (2) : 153-164.

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Acta Mathematica Sinica ›› 1999, Vol. 15 ›› Issue (2) : 153-164. DOI: 10.1007/BF02650658
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The Initial Boundary Value Problem for Navier-Stokes Equations

  • Cheng He
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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 uniformly C3 boundary, under the assumption that‖aL 2(Θ)+‖fL 1(0,∞;L2(Θ)) or‖▽aL 2(Θ)+‖f|L 2(0,∞;L2(Θ)) small or viscosityv large. Here a is a given initial velocity and f is the external force. This improves on the previous results. Moreover, the solvability of the case with nonhomogeneous boundary conditions is also discussed.

Key words

Navier-Stokes equations / Stokes equations / Homogeneous boundary conditions / Nonhomogeneous boundary conditions

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Cheng He. The Initial Boundary Value Problem for Navier-Stokes Equations. Acta Mathematica Sinica, 1999, 15(2): 153-164 https://doi.org/10.1007/BF02650658

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Funding

This work is supported by foundation of Institute of Mathematics, Academia Sinica
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