We consider the Cauchy problem of nonhomogeneous micropolar fluid equations with zero density at infinity on the whole space $\mathbb{R}^2$. By weighted energy method, we show the local existence and uniqueness of strong solutions provided that the initial density decays not too slowly at infinity.

中文翻译：

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具有非负密度的二维非齐次微极性流体方程Cauchy问题的强解

我们考虑了在整个空间$ \ mathbb {R} ^ 2 $上无穷大且密度为零的非齐次微极性流体方程的Cauchy问题。通过加权能量方法，我们证明了强解的局部存在性和唯一性，前提是初始密度在无穷远处的衰减不会太慢。