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of 87
pro vyhledávání: '"Collot, Charles"'
It is well-known that the two-dimensional Keller-Segel system admits finite time blowup solutions, which is the case if the initial density has a total mass greater than $8\pi$ and a finite second moment. Several constructive examples of such solutio
Externí odkaz:
http://arxiv.org/abs/2409.05363
Autor:
Collot, Charles, Zhang, Kaiqiang
We consider the parabolic-elliptic Keller-Segel system in spatial dimensions $d\geq3$, which corresponds to the mass supercritical case. Some solutions become singular in finite time, an important example being backward self-similar solutions. Herrer
Externí odkaz:
http://arxiv.org/abs/2406.11358
The Hartree-Fock equation admits homogeneous states that model infinitely many particles at equilibrium. We prove their asymptotic stability in large dimensions, under assumptions on the linearised operator. Perturbations are moreover showed to scatt
Externí odkaz:
http://arxiv.org/abs/2310.03442
Autor:
Collot, Charles, Germain, Pierre
We show global asymptotic stability of solitary waves of the nonlinear Schr\"odinger equation in space dimension 1. Furthermore, the radiation is shown to exhibit long range scattering if the nonlinearity is cubic at the origin, or standard scatterin
Externí odkaz:
http://arxiv.org/abs/2306.03668
Non-radiative solutions of energy critical wave equations are such that their energy in an exterior region $|x|>R+|t|$ vanishes asymptotically in both time directions. This notion, introduced by Duyckaerts, Kenig and Merle (J. Eur. Math. Soc., 2011),
Externí odkaz:
http://arxiv.org/abs/2211.16085
On channels of energy for the radial linearised energy critical wave equation in the degenerate case
Publikováno v:
International Mathematics Research Notices, 2022
Channels of energy estimates control the energy of an initial data from that which it radiates outside a light cone. For the linearised energy critical wave equation they have been obtained in the radial case in odd dimensions, first in $3$ dimension
Externí odkaz:
http://arxiv.org/abs/2211.16075
The kinetic wave equation arises in wave turbulence to describe the Fourier spectrum of solutions to the cubic Schroedinger equation. The equation has two Kolmogorov-Zakharov steady states corresponding to out-of-equilibrium cascades transferring for
Externí odkaz:
http://arxiv.org/abs/2208.00947
We consider the quadratic semilinear wave equation in six dimensions. This energy critical problem admits a ground state solution, which is the unique (up to scaling) positive stationary solution. We prove that any spherically symmetric solution, tha
Externí odkaz:
http://arxiv.org/abs/2201.01848