Research article

Blow-up criterion for the 3D nematic liquid crystal flows via one velocity and vorticity components and molecular orientations

  • Received: 05 October 2019 Accepted: 02 December 2019 Published: 16 December 2019
  • MSC : 35B65, 35Q35, 76A15

  • In this paper, we are devoted to investigating the blow-up criteria for the three dimensional nematic liquid crystal flows. More precisely, we proved that the smooth solution $(u, d)$ can be extended beyond T, provided that $\int_{0}^{T}(||\omega_{3}||_{L^{p}}^{\frac{2p}{2p-3}}+||u_{3}||_{L^{q}}^{\frac{2q}{q-3}} +||\nabla d||_{\dot{B}_{\infty, \infty}^{0}}^{2})d t < \infty, \frac{3}{2} < p\leq\infty, 3 < q\leq\infty.$

    Citation: Qiang Li, Baoquan Yuan. Blow-up criterion for the 3D nematic liquid crystal flows via one velocity and vorticity components and molecular orientations[J]. AIMS Mathematics, 2020, 5(1): 619-628. doi: 10.3934/math.2020041

    Related Papers:

  • In this paper, we are devoted to investigating the blow-up criteria for the three dimensional nematic liquid crystal flows. More precisely, we proved that the smooth solution $(u, d)$ can be extended beyond T, provided that $\int_{0}^{T}(||\omega_{3}||_{L^{p}}^{\frac{2p}{2p-3}}+||u_{3}||_{L^{q}}^{\frac{2q}{q-3}} +||\nabla d||_{\dot{B}_{\infty, \infty}^{0}}^{2})d t < \infty, \frac{3}{2} < p\leq\infty, 3 < q\leq\infty.$



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