Honam Mathematical Journal (호남수학학술지)

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REGULARITY OF 3D NAVIER-STOKES EQUATIONS WITH SPECTRAL DECOMPOSITION

  • Jeong, Hyosuk (Department of Mathematics, Chonnam National University)
  • Received : 2016.06.29
  • Accepted : 2016.07.04
  • Published : 2016.09.25
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Abstract

In this paper, we consider the global existence of strong solutions to the incompressible Navier-Stokes equations on the cubic domain in $R^3$. While the global existence for arbitrary data remains as an important open problem, we here provide with some new observations on this matter. We in particular prove the global existence result when ${\Omega}$ is a cubic domain and initial and forcing functions are some linear combination of functions of at most two variables and the like by decomposing the spectral basis differently.

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References

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