关键词: compressible micropolar fluids, Cauchy problem, global classical solutions, small density, vacuum

Abstract: This paper concerns the Cauchy problem of 3D compressible micropolar fluids in the whole space $\mathbb{R}^3$. For regular initial data with $m_0E_0$ is suitable small, where $m_0$ and $E_0$ represent the upper bound of initial density and initial energy, we prove that if $\rho_0\in L^{\gamma}\cap H^3$ with $\gamma \in (1, 6)$, then the problem possesses a unique global classical solution on $\mathbb{R}^3 \times [0, T]$ with any $T\in (0, \infty)$. It's worth noting that both the vacuum states and possible random largeness of initial energy are allowed.

Key words: compressible micropolar fluids, Cauchy problem, global classical solutions, small density, vacuum