111 citations · 276 across the 11 of their papers we have counts for
18 papers
On smooth inviscid vortices with fat tails
Pierre Raphaël, Ayman R. Saïd
We derive a family of degenerate vortices with non trivial swirls and fat tails which can be used to bifurcate both stationary and self similar solutions to the three dimensional a…
A Two-Soliton with Transient Turbulent Regime for the Cubic Half-wave Equation on The Real Line
Patrick Gérard, Enno Lenzmann, Oana Pocovnicu +1
We consider the focusing cubic half-wave equation on the real line We…
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…
Strongly interacting blow up bubbles for the mass critical NLS
Yvan Martel, Pierre Raphael
We construct a new class of multi-solitary wave solutions for the mass critical two dimensional nonlinear Schrodinger equation (NLS). Given any integer K>1, there exists a global (…
On melting and freezing for the 2d radial Stefan problem
Mahir Hadzic, Pierre Raphael
We consider the two dimensional free boundary Stefan problem describing the evolution of a spherically symmetric ice ball . We revisit the pioneering analysis of [2…
Codimension one threshold manifold for the critical gKdV equation
Yvan Martel, Frank Merle, Kenji Nakanishi +1
We construct the 'threshold manifold' near the soliton for the mass critical gKdV equation, completing results obtained in arXiv:1204.4625 and arXiv:1204.4624. In a neighborhood of…