Local and Global Analysis for Discontinuous Atmospheric Ekman Equations

In this paper, we extend the classical atmospheric Ekman equations to discontinuous differential equations of Ekman flows by considering the eddy viscosity with piecewise form. Local and global analysis for the corresponding discontinuous ODEs are studied respectively. In the section of local analysis, all the possible crossings of solutions are presented over the certain discontinuity linear subspaces associated with a curve. In the section of global analysis, crossings of solutions, bounded and unbounded solutions on dynamics are obtained.