This result states long-time existence of harmonic map heat flow into nonpositively curved targets: given (M,g) be a closed smooth Riemannian manifold, and let (N,h) be a compact smooth Riemannian manifold whose sectional curvature satisfies K N 0. For every smooth map u 0: M N,.... It is useful in harmonic map theory and elliptic regularity, where variational identities, curvature estimates, and compactness arguments control geometric objects.