In this paper, we prove a new blowup criterion for the strong solution to the Cauchy problem of three-dimensional micropolar fluid equation with vacuum. Specifically, we establish a blowup criterion in terms of \(L_{t}^{\infty }L_{x}^{q}\) of the density, where \(1< q<\infty \), and it is independent on the velocity of rotation of the microscopic particles.

中文翻译：

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三维可压缩粘性微极性流体真空柯西问题的新爆破准则

在本文中，我们证明了真空下三维微极性流体方程柯西问题强解的新爆破准则。具体来说，我们根据密度的\(L_{t}^{\infty }L_{x}^{q}\)建立一个爆炸准则，其中\(1< q<\infty \)，并且它是与微观粒子的旋转速度无关。