$\mathrm{L}^p$-based Sobolev theory on closed manifolds of minimal regularity: Vector-valued problems

This paper is the second part of a two-paper series, initiated in arXiv:2603.02163 for scalar PDEs on hypersurfaces, and is concerned with the well-posedness and $\mathrm{L}^p$-based Sobolev regularity of vector-valued PDEs of interest in fluid dynamics. This family of PDEs includes the (stationary)