596 citations · 1.2k across the 49 of their papers we have counts for
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Blow up for the critical gKdV equation III: exotic regimes
Yvan Martel, Frank Merle, Pierre Raphael
We consider the blow up problem in the energy space for the critical (gKdV) equation in the continuation of part I and part II. We know from part I that the unique and stable blow…
Scattering for radial, bounded solutions of focusing supercritical wave equations
Thomas Duyckaerts, Carlos Kenig, Frank Merle
In this paper, we consider the wave equation in space dimension 3 with an energy-supercritical, focusing nonlinearity. We show that any radial solution of the equation which is bou…
Blow up for the critical gKdV equation II: minimal mass dynamics
Yvan Martel, Frank Merle, Pierre Raphael
We fully revisit the near soliton dynamics for the mass critical (gKdV) equation. In Part I, for a class of initial data close to the soliton, we prove that only three scenario can…
Classification of radial solutions of the focusing, energy-critical wave equation
Thomas Duyckaerts, Carlos Kenig, Frank Merle
In this paper, we describe the asymptotic behaviour of globally defined solutions and of bounded solutions blowing up in finite time of the radial energy-critical focusing non-line…
On collapsing ring blow up solutions to the mass supercritical NLS
Frank Merle, Pierre Raphaël, Jeremie Szeftel
We consider the nonlinear Schrödinger equation in dimension and in the mass super critical and energy subcritical range $1+\frac 4N<p<\min\…
Profiles of bounded radial solutions of the focusing, energy-critical wave equation
Thomas Duyckaerts, Carlos Kenig, Frank Merle
In this paper we consider global and non-global bounded radial solutions of the focusing energy-critical wave equation in space dimension 3. We show that any of these solutions dec…