39 citations · 217 across the 35 of their papers we have counts for
44 papers
An exact Delaunay flux identity for compact equilibria in the liquid drop model
Averkios Averkiou, Manuel del Pino, Monica Musso
We revisit the construction of compact liquid drop equilibria from Delaunay unduloids in [Arch. Ration. Mech. Anal. 249 (2025), Paper No. 74]. We evaluate exactly the coefficient a…
A Supercritical Problem in Dimension Two
Manuel del Pino, Ignacio Guerra, Monica Musso
Let be a smooth bounded domain containing the origin and invariant under reflection across the coordinate axes, and let , where is the f…
Nondegeneracy of the Sadovskii vortex
M. del Pino, M. Musso, J. Wei
We prove nondegeneracy, modulo horizontal translation, of the normalized Sadovskii vortex patch. Building on the free-boundary and root-map framework developed by Huang and Tong, w…
On the vortex filament conjecture for the Gross-Pitaevskii equation
Manuel del Pino, Rowan Juneman, Monica Musso +1
We establish one form of the vortex filament conjecture for the three-dimensional Gross-Pitaevskii equation. Given any smooth closed embedded binormal flow of curves on a compact t…
A Bernstein problem for translating solutions to the mean curvature flow
Juan Davila, Manuel del Pino, Juncheng Wei
We study entire graphical translating solutions of the mean curvature flow, \[ \operatorname{div}\!\left(\frac{\nabla G}{\sqrt{1+|\nabla G|^2}}\right) =\frac{1}{\sqrt{1+|\nabla G|^…
The double sphere solution in the liquid drop model
Manuel del Pino, Rupert L. Frank, Monica Musso
We consider the problem of finding critical domains for the energy functional $$ \mathcal E (Ω) = {\rm Per}\,(Ω) + \frac 12 \iint_{Ω\times Ω} \frac{dx\,dy}{…
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 soluti…
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 \[ u_t=Δu+u^3, \qquad n\geq 5. \] 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}-Δv=|\nabla_x v|^2 \end{equation*} in dimensions , under radial symmetry. For every pre…
Existence of finite time blow-up in Keller-Segel system
Federico Buseghin, Juan Davila, Manuel del Pino +1
Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system $\begin{equation} \begin{cases} u_{t} =Δu - \nabla \cdot(u \nabla v) \ \ \ \text{in } \mathbb{R…
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 $$ ω_t + \nabla^\perp Ψ\cdot \nabla ω= 0 , \quad Ψ= (-Δ)^{-1} ω, \quad \hbox{in } \mathbb{R…
Global in Time Vortex Configurations for the D Euler Equations
Juan Dávila, Manuel del Pino, Monica Musso +1
We consider the problem of finding a solution to the incompressible Euler equations $$ ω_t + v\cdot \nabla ω= 0 \quad \hbox{ in } \mathbb{R}^2 \times (0,\infty), \quad v(x,t) = \fr…
Infinite time blow-up for the three dimensional energy critical heat equation in bounded domains
Giacomo Ageno, Manuel del Pino
We consider the Dirichlet problem for the energy-critical heat equation \begin{equation*} \begin{cases} u_t=Δu+u^5,~&\mbox{ in } Ω\times \mathbb{R}^+,\\ u(x,t)=0,~&\mbox{ on } \par…
Solutions of the Ginzburg-Landau equations concentrating on codimension-2 minimal submanifolds
Marco Badran, Manuel del Pino
We consider the magnetic Ginzburg-Landau equations in a compact manifold $$ \begin{cases} -\varepsilon^2 Δ^{A} u=\frac{1}{2}(1-|u|^2)u,\\ \varepsilon^2 d^*dA=\langle\nabla^A u,…
Leapfrogging vortex rings for the 3-dimensional incompressible Euler equations
Juan Davila, Manuel del Pino, Monica Musso +1
A classical problem in fluid dynamics concerns the interaction of multiple vortex rings sharing a common axis of symmetry in an incompressible, inviscid -dimensional fluid. Helm…
Entire solutions to 4-dimensional Ginzburg-Landau equations and codimension 2 minimal submanifolds
Marco Badran, Manuel del Pino
We consider the magnetic Ginzburg-Landau equations in $$ \begin{cases} -\varepsilon^2(\nabla-iA)^2u = \frac{1}{2}(1-|u|^{2})u,\\ \varepsilon^2 d^*dA = \langle(\nabla…
Existence and stability of infinite time bubble towers in the energy critical heat equation
Manuel del Pino, Monica Musso, Juncheng Wei
We consider the energy critical heat equation in for $$\left\{ \begin{aligned} u_t & = Δu+ |u|^{\frac 4{n-2}}u \hbox{ in }\ \mathbb R^n \times (0, \infty), \…
Type II blow-up in the 5-dimensional energy critical heat equation
Manuel del Pino, Monica Musso, Juncheng Wei
We consider the Cauchy problem for the energy critical heat equation $$ u_t = Δu + |u|^{\frac 4{n-2}}u {{\quad\hbox{in } }} \ {\mathbb R}^n \times (0, T), \quad u(\cdot,0) =u_0 {{\…
Geometry driven Type II higher dimensional blow-up for the critical heat equation
Manuel del Pino, Monica Musso, Juncheng Wei
We consider the problem v_t & = Δv+ |v|^{p-1}v \quad\hbox{in }\ Ω\times (0, T), v & =0 \quad\hbox{on } \partial Ω\times (0, T ) , v& >0 \quad\hbox{in }\ Ω\times (0, T) . In a domai…
Infinite time blow-up for the 3-dimensional energy critical heat equation
Manuel del Pino, Monica Musso, Juncheng Wei
We construct globally defined in time, unbounded positive solutions to the energy-critical heat equation in dimension three $$ u_t = Δu + u^5 , \quad {\mbox {in}} \quad \R^3 \times…
Singularity formation for the two-dimensional harmonic map flow into
Juan Davila, Manuel del Pino, Juncheng Wei
We construct finite time blow-up solutions to the 2-dimensional harmonic map flow into the sphere , \begin{align*} u_t & = Δu + |\nabla u|^2 u \quad \text{in } Ω\times(0,T) \\…
New type I ancient compact solutions of the Yamabe flow
Panagiota Daskalopoulos, Manuel del Pino, John King +1
We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as , to two self-similar complete non-compact s…
Interior bubbling solutions for the critical Lin-Ni-Takagi problem in dimension 3
Manuel del Pino, Monica Musso, Carlos Román +1
We consider the problem of finding positive solutions of the problem in a bounded, smooth domain in , under zero Neumann boundary conditions. H…