A new blowup criterion of strong solutions to the two‐dimensional equations of compressible nematic liquid crystal flows

Abstract

In this paper, we concern the Cauchy problem of two‐dimensional (2D) compressible nematic liquid crystal flows with vacuum as far‐field density. Under a geometric condition for the initial orientation field, we establish a blowup criterion in terms of the integrability of the density for strong solutions to the compressible nematic liquid crystal flows. This criterion generalizes previous results of compressible nematic liquid crystal flows with vacuum, which concludes the initial boundary problem and Cauchy problem.