Non-spherical minimizers in the generalized liquid drop model for Yukawa and truncated Coulomb potentials

2025/10/13 by Lia Bronsard, Bronsard, Lia, Benoît Merlet +3
Computer Science · Mathematics · Physics and Astronomy · #28A75 #49Q10 #49Q20 #49S05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2510.11893

openalex publication_date 2025/10/13 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

We investigate generalized liquid drop models with screened Riesz-type interactions, focusing in particular on truncated Coulomb and Yukawa potentials in three dimensions. While the classical Gamow model with Coulomb interaction is conjectured to admit only spherical minimizers below a critical mass and no minimizer above, we show that this conjecture fails if the interaction is screened. In the case of truncated Coulomb and Yukawa potentials, we establish the existence of non-spherical minimizers for some values of the screening parameter. This gives the first evidence of such minimizers in the class of repulsive, radial, and radially nonincreasing kernels in three dimensions. Our approach relies on a comparison of the energy-per-mass ratios of balls and cylinders, in contrast with recent two-dimensional results obtained via Γ-convergence. We further show that in the unscreened Riesz case, the conjecture remains consistent, though delicate. Indeed we observe that the energy-per-mass ratios of balls and of cylinders are surprisingly close.

Citations

• Euler's elastica functional as a large mass limit of a two-dimensional non-local isoperimetric problem
• A concentration-compactness principle for perturbed isoperimetric problems with general assumptions
• On minimizers in the liquid drop model
• Existence and nonexistence in the liquid drop model
• Anisotropic liquid drop models
• Periodic patterns for a model involving short-range and long-range\n interactions
• Droplet breakup in the liquid drop model with background potential
• A compactness lemma and its application to the existence of minimizers for the liquid drop model
• Small Volume Fraction Limit of the Diblock Copolymer Problem: II. Diffuse-Interface Functional

Related

• Existence of minimizers for a generalized liquid drop model with fractional perimeter
• Droplet breakup in the liquid drop model with background potential
• Large mass minimizers for isoperimetric problems with integrable nonlocal potentials
• A compactness lemma and its application to the existence of minimizers for the liquid drop model
• Existence and nonexistence in the liquid drop model