Sobolev regularity for the $\bar{\mathrm{\partial }}$-Neumann operator and transverse vector fields

On a bounded smooth pseudoconvex domain in ${\mathbb{C}}^n$ with $n>2$, inspired by the compactness condition introduced by Yue Zhang, we present the new sufficient condition for the exact regularity of the $\bar{\mathrm{\partial }}$-Neumann operator via the transverse vector fields.