9 papers
Nondegeneracy and Morse Index of Ginzburg--Landau Vortices
Manuel del Pino, Yong Liu, Monica Musso +2
We prove that the standard degree-two and degree-three vortex solutions of the Ginzburg-Landau equation are nondegenerate. Their Morse indices are also computed. The proof relies o…
A two-dimensional Allen-Cahn theory for interfaces with boundary
Marco Badran, Manuel del Pino, Marco A. M. Guaraco
We develop a two-dimensional Allen-Cahn theory for interfaces with boundary in the line-bundle framework introduced by Fröhlich and Struwe. The central new object is a model solut…
Collapsing-tube type II blow-up for the energy-supercritical heat equation
Manuel del Pino, Monica Musso, Juncheng Wei +1
We construct a new type II finite-time blow-up mechanism for the energy-supercritical heat equation \[ u_t=Îu+u^3, \qquad n\geq 5. \] The solution is positive and blows up only at…
Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation
Manuel del Pino, Oliver Gough, Monica Musso
We study finite-time blow-up for the nonlinear wave equation \begin{equation*} v_{tt}-Îv=|\nabla_x v|^2 \end{equation*} in dimensions , under radial symmetry. For every pr…
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…