5 papers
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…
Well-Posedness and Regularity of the Heat Equation with Robin Boundary Conditions in the Two-Dimensional Wedge
Marco Bravin, Manuel V. Gnann, Hans Knüpfer +3
Well-posedness and higher regularity of the heat equation with Robin boundary conditions in an unbounded two-dimensional wedge is established in an -setting of monomially we…
Blow-up of the one-dimensional wave equation with quadratic spatial derivative nonlinearity
Tej-eddine Ghoul, Jie Liu, Nader Masmoudi
We investigate the blow-up dynamics of smooth solutions to the one-dimensional wave equation with a quadratic spatial derivative nonlinearity, motivated by its applications in Effe…
Waiting Time Solutions in gas dynamics
Juhi Jang, Jiaqi Liu, Nader Masmoudi
In this article, we construct a continuum family of self-similar waiting time solutions for the one-dimensional compressible Euler equations for the adiabatic exponent $\ga\in(1,3)…
Blow-Up Dynamics for the critical case of the D Zakharov-Kuznetsov equation
Francisc Bozgan, Tej-Eddine Ghoul, Nader Masmoudi +1
We investigate the blow-up dynamics for the critical two-dimensional Zakharov-Kuznetsov equation \begin{equation*} \begin{cases} \partial_t u+\partial_{x_1} (Îu+u^3)=0, \mbo…