5 papers · 1 filter
Global in Time Vortex Configurations for the D Euler Equations
Juan Dávila, Manuel del Pino, Monica Musso +1
We consider the problem of finding a solution to the incompressible Euler equations $$ Ï_t + v\cdot \nabla Ï= 0 \quad \hbox{ in } \mathbb{R}^2 \times (0,\infty), \quad v(x,t) = \…
Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system
Federico Buseghin, Juan Dávila, Manuel del Pino +1
We construct axially symmetric finite-time blow-up solutions to the three-dimensional Keller-Segel system. By adapting gluing techniques, we derive a precise asymptotic expansion f…
An Expanding Self-Similar Vortex Configuration for the 2D Euler Equations
Juan Dávila, Manuel del Pino, Monica Musso +1
This paper addresses the long-time dynamics of solutions to the 2D incompressible Euler equations. We construct solutions with continuous vorticity concentr…
Overhanging solitary water waves
Juan Dávila, Manuel del Pino, Monica Musso +1
We provide the first construction of overhanging gravity water waves having the approximate form of a disk joined to a strip by a thin neck. The waves are solitary with constant vo…
Asymptotic properties of vortex-pair solutions for incompressible Euler equations in
Juan Dávila, Manuel del Pino, Monica Musso +1
A {\em vortex pair} solution of the incompressible Euler equation in vorticity form $$ Ï_t + \nabla^\perp Ψ\cdot \nabla Ï= 0 , \quad Ψ= (-Î)^{-1} Ï, \quad \hbox{in } \ma…