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\(L^\infty \) continuation principle to the compressible non-isothermal nematic liquid crystal flows with zero heat conduction and vacuum

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Abstract

We present a continuation principle for two-dimensional compressible non-isothermal nematic liquid crystal flows with zero heat conduction. We show that the concentration of the density or the pressure occurs in finite time for a large class of smooth initial data, which is responsible for the breakdown of strong solutions. It also gives an affirmative answer to a strong version of a problem proposed by J. Nash in 1950s.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Xin Zhong

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  1. Xin Zhong
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Correspondence to Xin Zhong.

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Communicated by M. Struwe.

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This research was partially supported by National Natural Science Foundation of China (Nos. 11901474, 12071359), Exceptional Young Talents Project of Chongqing Talent (No. cstc2021ycjh-bgzxm0153), the Innovation Support Program for Chongqing Overseas Returnees (Nos. cx2019130, cx2020082), and Natural Science Foundation of Chongqing (No. cstc2018jcyjAX0049).

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Zhong, X. \(L^\infty \) continuation principle to the compressible non-isothermal nematic liquid crystal flows with zero heat conduction and vacuum. Calc. Var. 61, 174 (2022). https://doi.org/10.1007/s00526-022-02290-9

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