7 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…
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 $$ \mathcal E (Ω) = {\rm Per}\,(Ω) + \frac 12 \iint_{Ω\times Ω} \frac{dx\,dy}{…
Symmetry Breaking and Moduli for Ancient Yamabe Flows on the Sphere
Haixia Chen, Seunghyeok Kim, Monica Musso
For every , we construct compact Type II ancient Yamabe flows in the round conformal class of the unit -sphere $\Ss^n$. After stereographic projection and rescaling of ti…
Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation
Manuel del Pino, Oliver Gough, Monica Musso
We study finite-time blow-up for the nonlinear wave equation \begin{equation*} v_{tt}-Δv=|\nabla_x v|^2 \end{equation*} in dimensions , under radial symmetry. For every pre…
Bifurcations in Isoperimetric Problems with Nonlocal Interactions
Fabio De Regibus, Massimo Grossi, Monica Musso
We study isoperimetric problems modeled on the liquid drop model, with nonlocal interactions under a volume constraint. While balls are natural critical points, we show that, for a…
Clustered vortex helices with compactly supported cross-sectional vorticity in the 3D Euler equations
Averkios Averkiou, Monica Musso, Fang Yu
We consider the three-dimensional incompressible Euler equations for helical flows without swirl. By adapting gluing techniques, we construct the first smooth multi-vortex solution…
Nodal cluster solutions for the Brezis-Nirenberg problem in dimensions
Monica Musso, Serena Rocci, Giusi Vaira
We show that the classical Brezis-Nirenberg problem $$Δu + |u|^{4 \over N-2} u + \varepsilon u = 0 ,\quad {\mbox {in}} \quad Ω, \quad u= 0 , \quad {\mbox {on}} \quad \partial Ω$$ a…