Pierre Raphael

most citedBlow up dynamics for smooth data equivariant solutions to the energy critical Schrodinger map problem

15 citations · 27 across the 3 of their papers we have counts for

collaborators

3 papers

math.AP2011

Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map

Frank Merle, Pierre Raphaël, Igor Rodnianski

We consider the energy critical Schrödinger map problem with the 2-sphere target for equivariant initial data of homotopy index $k = 1$ . We show the existence of a codimension one se…

math.AP2011★ 15 cited

Blow up dynamics for smooth data equivariant solutions to the energy critical Schrodinger map problem

Frank Merle, Pierre Raphael, Igor Rodnianski

We consider the energy critical Schrodinger map to the 2-sphere for equivariant initial data of homotopy number k=1. We show the existence of a set of smooth initial data arbitrari…

math.AP2010★ 12 cited

Smooth type II blow up solutions to the four dimensional energy critical wave equation

Matthieu Hillairet, Pierre Raphaël

We exhibit $C^{\infty}$ type II blow up solutions to the focusing energy critical wave equation in dimension $N = 4$ . These solutions admit near blow up time a decomposiiton…