Construction of concentrating bubbles for the energy-critical wave equation

If, in addition, we assume that the critical norm of the evolution localized to the light cone (the forward light cone in the case of global solutions and the backwards cone in the

We consider the radial free wave equation in all dimensions and derive asymptotic formulas for the space partition of the energy, as time goes to infinity.. We show that the

The equations covered by our results include the 2 dimensional corotational wave map system, with target S 2 , in the critical energy space, as well as the 4 dimensional,

As a consequence, we can study the flow of (mKdV) around self-similar solutions: in particular, we give an as- ymptotic description of small solutions as t → +∞ and construct

Clearly if the Cauchy problem for the Yang-Mills equation (2.14) on a globally hyperbolic spacetime (M, g) can be globally solved in the space of smooth space-compact solutions,

We prove the uniqueness of weak solutions to the critical defocusing wave equation in 3D under a local energy inequality condition.. Uniqueness was proved only under an

Existence of a stable blow-up profile for the nonlinear heat equation with a critical power nonlinear gradient term. Higher-dimensional blow up for semilinear parabolic

Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schr¨ odinger equation in the radial case.. Kenig and