Minimal blow-up masses and existence of solutions for an asymmetric sinh-Poisson equation

TL;DR

This paper establishes optimal blow-up mass bounds for an asymmetric sinh-Poisson equation and uses these results to construct mountain pass solutions on 2D tori, advancing understanding in hydrodynamic turbulence models.

Contribution

It provides the first optimal lower bounds for blow-up masses in asymmetric sinh-Poisson equations and constructs solutions using mountain pass techniques.

Findings

Optimal blow-up mass bounds established

Existence of mountain pass solutions on 2D tori demonstrated

Contributes to mathematical understanding of turbulence models

Abstract

For a sinh-Poisson type problem with asymmetric exponents of interest in hydrodynamic turbulence, we establish the optimal lower bounds for the blow-up masses. We apply this result to construct solutions of mountain pass type on two-dimensional tori.