A blowup criterion for the compressible nematic liquid crystal flows in dimension two

A regularity condition of strong solutions to the two‐dimensional equations of compressible nematic liquid crystal flows

“…More recently, the similar results have been obtained by Huang-Huang [15] for incompressible case and by Gao-Tao-Yao [16] for compressible case in a bounded domain of dimension two, respectively. First, we explain the conventions and notations used in what follows.…”

“…Compared with Gao-Tao-Yao's [16] result, they can get any L p -norm of u .p 1/ because the domain is bounded. However, it is impossible for Cauchy problem, in order to overcome this difficulty, we need some weighted estimates of the velocity u.…”

“…Let ( ρ , u , d ) be a strong solution to the Cauchy problem , , and , satisfying . If T ∗ < ∞ is the maximal time of existence, then with r and s satisfy Remark Compared with Gao‐Tao‐Yao's result, they can get any L p ‐norm of u ( p ≥1) because the domain is bounded. However, it is impossible for Cauchy problem, in order to overcome this difficulty, we need some weighted estimates of the velocity u .…”

A new blowup criterion for strong solutions of the compressible nematic liquid crystal flow

“…where 2 si + n ri ≤ 1, n < r i ≤ ∞, i = 1, 2 and n is the spatial dimension. For two dimensions, Gao-Tao-Yao [7] established a Serrin-type blowup criterion for initialboundary value problem of (1.1)-(1.3) as follows,…”

Asymptotic Behavior of Solution to the Incompressible Nematic Liquid Crystal Flows in R^3

“…For more results, the readers can refer to [28] that have introduced some recent developments of analysis for hydrodynamic flow of nematic liquid crystal flows and references therein. As for the compressible nematic liquid crystal flows, the readers can refer to [29][30][31][32][33][34][35][36][37][38][39][40][41] and references therein.…”