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math.AP2024
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…
math.AP2024
Blow-Up Dynamics for the critical case of the D Zakharov-Kuznetsov equation
Francisc Bozgan, Tej-Eddine Ghoul, Nader Masmoudi +1
We study blow-up dynamics for the -critical cubic Zakharov--Kuznetsov equation in two dimensions, \[ \partial_tu+\partial_{x_1}(Δu+u^3)=0 \qquad\text{on }\mathbb R^2. \] For a…