Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ON MIXED PRESSURE-VELOCITY REGULARITY CRITERIA FOR THE 3D MICROPOLAR EQUATIONS IN LORENTZ SPACES

  • Kim, Jae-Myoung (Department of Mathematics Education Andong National University) ;
  • Kim, Jaewoo (Department of Mathematics Yonsei University)
  • Received : 2020.11.09
  • Accepted : 2021.02.08
  • Published : 2021.02.15
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Abstract

In present paper, inspired by the recently paper [1], we give the mixed pressure-velocity regular criteria in view of Lorentz spaces for weak solutions to 3D micropolar equations in a half space. Precisely, if (0.1) ${\frac{P}{(e^{-{\mid}x{\mid}^2}+{\mid}u{\mid})^{\theta}}{\in}L^p(0,T;L^{q,{\infty}}({\mathbb{R}}^3_+))$, p, q < ∞, and (0.2) ${\frac{2}{p}}+{\frac{3}{q}}=2-{\theta}$, 0 ≤ θ ≤ 1, then (u, w) is regular on (0, T].

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Acknowledgement

Jae-Myoung Kim's work is supported by a Research Grant of Andong National University.

References

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