596 citations · 1.2k across the 49 of their papers we have counts for
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Universality of blow up profile for small blow up solutions to the energy critical wave map equation
Thomas Duyckaerts, Hao Jia, Carlos Kenig +1
In this paper we introduce the channel of energy argument to the study of energy critical wave maps into the sphere. More precisely, we prove a channel of energy type inequality fo…
Blow-up solutions to the semilinear wave equation with a stylized pyramid as a blow-up surface
Frank Merle, Hatem Zaag
We consider the semilinear wave equation with subconformal power nonlinearity in two space dimensions. We construct a finite-time blow-up solution with an isolated characteristic b…
Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions
Charles Collot, Frank Merle, Pierre Raphael
We consider the energy critical semilinear heat equation and give a complete classification of the flow near the groun…
Scattering profile for global solutions of the energy-critical wave equation
Thomas Duyckaerts, Carlos Kenig, Frank Merle
Consider the focusing energy-critical wave equation in space dimension 3, 4 or 5. We prove that any global solution which is bounded in the energy space converges in the exterior o…
Soliton resolution along a sequence of times for the focusing energy critical wave equation
Thomas Duyckaerts, Hao Jia, Carlos Kenig +1
In this paper, we prove the soliton resolution conjecture for general type II solutions to the focusing energy critical wave equation, in space dimension 3,4 or 5, along a sequence…