A flow on \begin{document}$ S^2 $\end{document} presenting the ball as its minimal set

The main goal of this paper is to present the existence of a vector field tangent to the unit sphere \begin{document}$ S^2 $\end{document} such that \begin{document}$ S^2 $\end{document} itself is a minimal set. This is reached using a piecewise smooth (discontinuous) vector field and following the Filippov's convention on the switching manifold. As a consequence, none regularization process applied to the initial model can be topologically equivalent to it and we obtain a vector field tangent to \begin{document}$ S^2 $\end{document} without equilibria.