Existence and nonexistence in the liquid drop model

TL;DR

This paper investigates the liquid drop model with a Riesz potential, establishing the existence of minimizers within certain parameters, proving conditional uniqueness, and demonstrating nonexistence for heavy nuclei.

Contribution

It provides new existence results for minimizers in the liquid drop model with Riesz potential and explores conditions for uniqueness and nonexistence.

Findings

Existence of minimizers in a specific parameter range.

Conditional uniqueness of minimizers.

Nonexistence results for heavy nuclei.

Abstract

We revisit the liquid drop model with a general Riesz potential. Our new result is the existence of minimizers for the conjectured optimal range of parameters. We also prove a conditional uniqueness of minimizers and a nonexistence result for heavy nuclei.