17 citations · 80 across the 8 of their papers we have counts for
10 papers
Modulation algorithm for the nonlinear Schr{ö}dinger equation
Erwan Faou, Yoann Le Henaff, Pierre Raphaël
Based on recent ideas, stemming from the use of bubbles, we discuss an algorithm for the numerical simulation of the cubic nonlinear Schr{ö}dinger equation with harmonic potential…
On smooth self similar solutions to the compressible Euler equations
Frank Merle, Pierre Raphael, Igor Rodnianski +1
We consider the barotropic Euler equations in dimension d>1 with decaying density at spatial infinity. The phase portrait of the nonlinear ode governing the equation for sphericall…
On the implosion of a three dimensional compressible fluid
Frank Merle, Pierre Raphael, Igor Rodnianski +1
We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data f…
On strongly anisotropic type II blow up
Charles Collot, Frank Merle, Pierre Raphael
We consider the energy super critical dimensional semilinear heat equation A fundamental open proble…
On strongly anisotropic type I blow up
Frank Merle, Pierre Raphael, Jeremie Szeftel
We consider the energy super critical 4 dimensional semilinear heat equation Let be a three dimensional radial sel…
On the stability of type I blow up for the energy super critical heat equation
Charles Collot, Pierre Raphael, Jeremie Szeftel
We consider the energy super critical semilinear heat equation We first revisit the construction of radially symmetric bac…