F. Merle

activity

20012026

most citedGlobal well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case

596 citations · 1.2k across the 49 of their papers we have counts for

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Showing 2017 · math.APShow all

3 papers · 2 filters

math.AP2017★ 11 cited

On strongly anisotropic type II blow up

Charles Collot, Frank Merle, Pierre Raphael

We consider the energy super critical $d + 1$ dimensional semilinear heat equation $\partial_{t} u = Δ u + u^{p}, x \in R^{d + 1}, p \geq 3, d \geq 14.$ A fundamental open proble…

math.AP2017

On strongly anisotropic type I blow up

Frank Merle, Pierre Raphael, Jeremie Szeftel

We consider the energy super critical 4 dimensional semilinear heat equation $\partial_{t} u = Δ u + ∣ u ∣^{p - 1} u, x \in R^{4}, p > 5.$ Let $Φ (r)$ be a three dimensional radial sel…

math.AP2017★ 19 cited

Inelasticity of soliton collisions for the 5D energy critical wave equation

Yvan Martel, Frank Merle

For the focusing energy critical wave equation in 5D, we construct a solution showing the inelastic nature of the collision of any two solitons, except the special case of two soli…