Elsevier

Journal of Differential Equations

Volume 267, Issue 6, 5 September 2019, Pages 3797-3826
Journal of Differential Equations

Singularity formation to the two-dimensional compressible non-isothermal nematic liquid crystal flows in a bounded domain☆

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Abstract

We study the singularity formation of strong solutions to the two-dimensional (2D) compressible non-isothermal nematic liquid crystal flows in a bounded domain. Under a geometric condition of the initial orientation field, we show that the strong solution exists globally if the temporal integral of the maximum norm of the divergence of the velocity is bounded. Our method relies on critical Sobolev inequalities of logarithmic type and delicate energy estimates.

MSC

76W05
76N10

Keywords

Compressible non-isothermal nematic liquid crystal flows
Strong solutions
Blow-up criterion

Cited by (0)

☆

Supported by Fundamental Research Funds for the Central Universities (No. XDJK2019B031), Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2018jcyjAX0049), the Postdoctoral Science Foundation of Chongqing (No. xm2017015), and China Postdoctoral Science Foundation (Nos. 2018T110936, 2017M610579).

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