Global strong solution to the nonhomogeneous micropolar fluid equations with large initial data and vacuum

Abstract

<p style='text-indent:20px;'>We study the Cauchy problem of nonhomogeneous micropolar fluid equations with zero density at infinity in the whole plane <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^2 $\end{document}</tex-math></inline-formula>. We derive the global existence and uniqueness of strong solutions if the initial density decays not too slowly at infinity. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Our method relies upon the delicate weighted energy estimates and the structural characteristics of the system under consideration.</p>

Global solvability to the 3D incompressible magneto-micropolar system with vacuum

“…Meanwhile, Wu and Zhong [16] established similar results in bounded domain. Recently, for the Cauchy problem in the whole 2D space, the authors independently obtained the global strong solutions for large initial data, see [12,23].…”