Pierre Raphaël

activity

20062009

most citedTwo soliton solutions to the three dimensional gravitational Hartree equation

9 citations · 20 across the 4 of their papers we have counts for

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4 papers · 1 filter

math.AP2009★ 7 cited

Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills problems

P. Raphael, I. Rodnianski

We exhibit stable finite time blow up regimes for the energy critical co-rotational Wave Map with the S^2 target in all homotopy classes and for the critical equivariant SO(4) Yang…

math.AP2009★ 1 cited

Stable self similar blow up dynamics for slightly L^2 supercritical NLS equations

Frank Merle, Pierre Raphael, Jeremie Szeftel

We consider the focusing nonlinear Schrödinger equations $i \partial_{t} u + Δ u + u ∣ u ∣^{p - 1} = 0$ in dimension $1 \leq N \leq 5$ and for slightly $L^{2}$ supercritical nonlinearities $p_c<p<(1…

math.AP2008★ 9 cited

Two soliton solutions to the three dimensional gravitational Hartree equation

Joachim Krieger, Yvan Martel, Pierre Raphael

We construct non dispersive two soliton solutions to the three dimensional gravitational Hartree equation whose trajectories asymptotically reproduce the nontrapped dynamics of the…

math.AP2006★ 3 cited

Blow up of the critical norm for some radial L^2 super critical nonlinear Schrodinger equations

Frank Merle, Pierre Raphael

We consider the nonlinear Schrödinger equation $i u_{t} = - Δ u - ∣ u ∣^{p - 1} u$ in dimension $N \geq 3$ in the $L^{2}$ super critical range $1 + \frac{4}{N} < p < \frac{N + 2}{N - 2}$ . The corresponding s…