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- W2805602012 abstract "Abstract In this paper, we study the possible singular set of suitable weak solutions ( u , d ) to the 3d simplified nematic liquid crystal flows, and prove that the parabolic upper Minkowski dimension of the possible singular set is bounded by 95 63 . Moreover, if the suitable weak solution ( u , d ) of the 3d simplified nematic liquid crystal flows satisfies ( u , ∇ d ) ∈ L w ( 0 , T ; L s ( R 3 ) ) with 3 w , s ∞ , then the parabolic upper Minkowski dimension of the singular set is no greater than max { w , s } ( 2 w + 3 s − 1 ) . If the suitable weak solution ( u , d ) satisfies ( u , ∇ d ) ∈ L ∞ ( 0 , T ; L 3 , ∞ ( R 3 ) ) , where L 3 , ∞ ( R 3 ) denotes the standard weak L 3 -Lebesgue space, then the parabolic upper Minkowski dimension of the singular set is bounded by 1." @default.
- W2805602012 created "2018-06-13" @default.
- W2805602012 creator A5042861108 @default.
- W2805602012 date "2018-12-01" @default.
- W2805602012 modified "2023-09-29" @default.
- W2805602012 title "Dimension of singularities to the 3d simplified nematic liquid crystal flows" @default.
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- W2805602012 doi "https://doi.org/10.1016/j.nonrwa.2018.05.005" @default.
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