The Initial Boundary Value Problem for Navier-Stokes Equations
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Acta Mathematica Sinica, English Series  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
Institute of Applied Mathmatics, Academia Sinica, Beijing 100080, P. R. China
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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.
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Cheng He
Key wordsNavier-Stokes equations   Stokes equations   Homogeneous boundary conditions   Nonhomogeneous boundary conditions     
Received: 1994-04-07;
Fund: This work is supported by foundation of Institute of Mathematics, Academia Sinica
Cite this article:   
Cheng He. The Initial Boundary Value Problem for Navier-Stokes Equations[J]. Acta Mathematica Sinica, English Series, 1999, 15(2): 153-164.
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http://www.actamath.com/Jwk_sxxb_en//EN/10.1007/BF02650658      or     http://www.actamath.com/Jwk_sxxb_en//EN/Y1999/V15/I2/153
 
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