Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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LOCAL REGULARITY OF THE STEADY STATE NAVIER-STOKES EQUATIONS NEAR BOUNDARY IN FIVE DIMENSIONS

  • Kim, Jaewoo (Department of Mathematics Sungkyunkwan University) ;
  • Kim, Myeonghyeon (Department of Mathematics Sungkyunkwan University)
  • Received : 2009.06.29
  • Accepted : 2009.08.14
  • Published : 2009.09.30
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Abstract

We present a new regularity criterion for suitable weak solutions of the steady-state Navier-Stokes equations near boundary in dimension five. We show that suitable weak solutions are regular up to the boundary if the scaled $L^{\frac{5}{2}}$-norm of the solution is small near the boundary. Our result is also valid in the interior.

Keywords

References

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