Communications in Mathematical Sciences
Volume 19 (2021)
$L^\infty$ continuation principle for two-dimensional compressible nematic liquid crystal flows
Pages: 55 – 72
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.
compressible nematic liquid crystal flows, strong solutions, blow-up criterion
2010 Mathematics Subject Classification
35B65, 76A15, 76N10
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