5 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…
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…
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…
Vortex dynamics for the Gross-Pitaevskii equation
Manuel del Pino, Rowan Juneman, Monica Musso
We rigorously establish the formal asymptotics of Neu for Gross-Pitaevskii vortex dynamics in the plane. Given any integer , we construct a family of -vortex solutions w…