We consider wave maps from the \((1+d)\) -dimensional Minkowski space into the d-sphere. It is known from the work of Bizoń and Biernat (Commun Math Phys 338(3): 1443–1450, 2015) that in the energy-supercritical case, i.e., for \(d \ge 3\) , this model admits a closed-form corotational self-similar blowup solution. We show that this blowup profile is globally nonlinearly stable for all \(d \ge 3\) , thereby verifying a perturbative version of the conjecture posed in Bizoń and Biernat (Commun Math Phys 338(3): 1443–1450, 2015) about the generic large data blowup behavior for this model. To accomplish this, we develop a novel stability analysis approach based on similarity variables posed on the whole space \(\mathbb {R}^d\) . As a result, we draw a general road map for studying spatially global stability of self-similar blowup profiles for nonlinear wave equations in the radial case for arbitrary dimension \(d \ge 3\) .
