Gorenstein projective and weak Gorenstein flat modules

Let R be a ring such that all flat R-modules have finite strongly FP-injective dimension. We obtain that the class of all Gorenstein projective modules forms a left-hand class of complete and hereditary cotosion pair. As applications, we prove that the same behavior holds for the class of all weak Gorenstein flat modules. We also obtain a characterization of global Gorenstein flat-cotorsion dimension of rings in terms of weak Gorenstein flat modules.