Discontinuous differential equation for modelling the Antarctic Circumpolar Current

Abstract

In this paper, we were concerned with the existence of the solution related to the discontinuous differential equation, which corresponded to the stratification phenomenon in the Antarctic Circumpolar Current (ACC). By considering the piecewise vorticity function, we demonstrated the existence of solution corresponding to the discontinuous differential equation using Green's function, fixed point theory, and topological degree theory. This primarily included cases with piecewise constant vorticity, piecewise linear vorticity, and piecewise nonlinear vorticity. Additionally, we provided some examples to verify our results.

Keywords

• antarctic circumpolar current
• stratification
• green's function
• discontinuous differential equation
• topological degree theory