Pierre Raphael

activity

20102023

most citedOn smooth self similar solutions to the compressible Euler equations

17 citations · 80 across the 8 of their papers we have counts for

collaborators

Showing 2017Show all

2 papers · 1 filter

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…