This is the main paper in a sequence in which we give a complete proof of the bounded L^ 2
L 2 curvature conjecture. More precisely we show that the time of existence of a classical …

Regularity of Wave-Maps in Dimension 2 + 1 Page 1 Digital Object Identifier (DOI) 10.1007/s00220-010-1062-3
Commun. Math. Phys. 298, 231–264 (2010) Communications in Mathematical Physics …

Following our previous paper in the radial case, we consider type II blow-up solutions to the
energy-critical focusing wave equation. Let W be the unique radial positive stationary …

In this paper, we prove that any solution of the energy-critical wave equation in space
dimensions 3, 4 or 5, which is bounded in the energy space decouples asymptotically, for a …

In this article we consider large data Wave-Maps from\mathbb R^ 2+ 1 into a compact
Riemannian manifold (M, g), and we prove that regularity and dispersive bounds persist as …

We consider the energy-critical wave maps equation R^ 1+ 2 → S^ 2 R 1+ 2→ S 2 in the
equivariant case, with equivariance degree k ≥ 2 k≥ 2. It is known that initial data of …

We consider finite energy corotational wave maps with target manifold. We prove that for a
sequence of times, they decompose as a sum of decoupled harmonic maps in the light cone …

We consider $1 $-equivariant wave maps from ${\Bbb R}^{1+ 2}\to {\Bbb S}^ 2$. For wave
maps of topological degree zero we prove global existence and scattering for energies …

This is a survey of the theory of attractors of nonlinear Hamiltonian partial differential
equations since its appearance in 1990. Included are results on global attraction to …

This article is devoted to the energy critical hyperbolic Yang–Mills equation in the $(4+ 1) $-
dimensional Minkowski space, which is considered by the authors in a sequence of four …