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

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 sigma is an element of(1,32]$$ \sigma \in \left(1,\frac{3}{2}\right] $$. 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 x$$ x $$-variable.