7 papers · 1 filter
Singularity formed by the collision of two collapsing solitons in interaction for the 2D Keller-Segel system
Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi +1
It is well-known that the two-dimensional parabolic-elliptic Keller-Segel system admits finite-time blowup solutions, which is the case if the initial density has total mass greate…
Classification of the dynamics of radial solutions to the 2D parabolic-elliptic Keller-Segel System
Federico Buseghin, Charles Collot
This note gives a complete classification of the asymptotic behavior of radial solutions to the two-dimensional parabolic-elliptic Keller-Segel system on the whole space, for gener…
Determination of the long-time dynamics for the 2D Keller-Segel equation at critical mass
Federico Buseghin, Charles Collot
We consider the parabolic-elliptic Keller-Segel equation in two dimensions on the whole space. We prove that for arbitrary initial data with critical mass and finite second m…
Stable self-similar singularity formation for infinite energy solutions of the incompressible porous medium equations
Charles Collot, Christophe Prange, Jin Tan
We consider a special class of infinite energy solutions to the inviscid incompressible porous medium equations (IPM), introduced in Castro-Córdoba-Gancedo-Orive [9]. The (IPM) eq…
Absence of embedded spectrum for nonlinear Schrödinger equations linearized around one dimensional ground states
Charles Collot, Pierre Germain, Eliot Pacherie
We consider the nonlinear Schrödinger equation in dimension one for a generic nonlinearity. We show that ground states do not have embedded eigenvalues in the essential spectrum o…
Estimates for the Gross-Pitaevskii equation linearized around a vortex
Charles Collot, Pierre Germain, Eliot Pacherie
We consider the linearized two-dimensional Gross-Pitaevskii equation around a vortex of degree one, with data in the same equivariance class. Various estimates are proved for the s…