Local Well‐Posedness to the Magneto‐Micropolar Boundary Layer Equations in Gevrey Space

ABSTRACT We study the boundary layer equations for two‐dimensional magneto‐micropolar boundary layer system and establish the existence and uniqueness of solutions in the Gevrey function space without any structural assumption, with Gevrey index . Inspired by the abstract Cauchy‐Kovalevskaya theorem, our proof is based on a new cancellation mechanism in the system to overcome the difficulties caused by the loss of derivatives. Our results improve the classical local well‐posedness results presented in a previous study, specifically for cases where the initial data are analytic in the ‐variable.