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.

中文翻译：

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二维可压缩向列液晶流的$ L ^ \ infty $延续原理

我们考虑二维（2D）可压缩向列液晶流的初始边界值问题。在初始定向场的几何条件下，我们表明，如果密度是从上方限制的，则强解整体存在。我们的证明依赖于基本能量估计和对数类型的临界Sobolev不等式。