Global well-posedness to the nonhomogeneous magneto-micropolar fluid equations with large initial data and vacuum

Abstract

<p style='text-indent:20px;'>We investigate global well-posedness to nonhomogeneous magneto-micropolar fluid equations with zero density at infinity in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^2 $\end{document}</tex-math></inline-formula>. We show the global existence and uniqueness of strong solutions. It should be pointed out that the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Our method relies crucially upon the duality principle of BMO space and Hardy space, a lemma of Coifman-Lions-Meyer-Semmes (Coifman et al. in J Math Pures Appl 72: 247–286, 1993), and cancelation properties of the system under consideration.</p>