596 citations · 1.2k across the 49 of their papers we have counts for
8 papers · 2 filters
Scattering for H^1/2 bounded solutions to the cubic, defocusing NLS in 3 dimensions
Carlos E. Kenig, Frank Merle
We show that if a solution of the defocusing cubic NLS in 3d remains bounded in the homogeneous Sobolev norm of order 1/2 in its maximal interval of existence, then the interval is…
Dynamic of threshold solutions for energy-critical wave equation
Thomas Duyckaerts, Frank Merle
We consider the energy-critical non-linear focusing wave equation in dimension N=3,4,5. An explicit stationnary solution, , of this equation is known. The energy E(W,0) has been…
Dynamic of threshold solutions for energy-critical NLS
Thomas Duyckaerts, Frank Merle
We consider the radial energy-critical non-linear focusing Schrödinger equation in dimension N=3,4,5. An explicit stationnary solution, W, of this equation is known. In a previous…
Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system
Raphael Cote, Carlos E. Kenig, Frank Merle
We describe the asymptotic behavior as time goes to infinity of solutions of the 2 dimensional corotational wave map system and of solutions to the 4 dimensional, radially symmetri…
Stability of two soliton collision for nonintegrable gKdV equations
Yvan Martel, Frank Merle
We continue our study of the collision of two solitons for the subcritical generalized KdV equations. In a previous paper, mainly devoted to the case of the quartic gKdV equation,…
Description of two soliton collision for the quartic gKdV equation
Yvan Martel, Frank Merle
This paper concerns the problem of collision of two solitons for the quartic generalized Korteweg-de Vries equation. We introduce a new framework to describe the collision in the s…