3 papers
math.AP2026
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…
math.AP2026
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…
math.AP2026
On the Classification of blow-up solutions of a singular Liouville equation on the disk
Zhijie Chen, Houwang Li, Tuoxin Li +1
We study the blow-up behavior of solutions to the singular Liouville equation \[ Î\tilde u+λe^{\tilde u}=4Ïαδ_0 \quad\text{in }B,\quad \tilde u=0 \quad\text{on }\partial B, \]…