Global existence and uniqueness of solutions to the Prandtl-Hartmann boundary layer equations

In this paper, we consider the global existence and uniqueness of solutions to the 2D Prandtl-Hartmann boundary layer equations on the upper half plane by using the classical energy methods in analytic framework. Then, we prove the lifespan of the solutions to the 2D Prandtl-Hartmann equations can be extended up to $ T_\varepsilon $ when the norm of the initial datum is of the order of $ \varepsilon $.