$L^\infty$ continuation principle for two-dimensional compressible nematic liquid crystal flows

We consider an initial boundary value problem of two-dimensional (2D) compressible nematic liquid crystal flows. Under a geometric condition for the initial orientation field, we show that the strong solution exists globally if the density is bounded from above. Our proof relies on elementary energy estimates and critical Sobolev inequalities of logarithmic type.

Keywords

compressible nematic liquid crystal flows, strong solutions, blow-up criterion

2010 Mathematics Subject Classification

35B65, 76A15, 76N10

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The author was supported by the National Natural Science Foundation of China (No. 11901474).

Received 9 June 2018

Accepted 30 July 2020

Published 24 March 2021