# Optimal estimates for far field asymptotics of solutions to the quasi-geostrophic equation

## TL;DR

This paper provides uniform estimates for the far field asymptotics of solutions to the critical and supercritical two-dimensional dissipative quasi-geostrophic equation, highlighting the slow decay due to anomalous diffusion.

## Contribution

It offers new uniform estimates for the far field behavior of solutions, advancing understanding of decay properties in critical and supercritical cases.

## Key findings

- Established uniform estimates for solutions' far field asymptotics
- Demonstrated slow decay of solutions due to anomalous diffusion
- Enhanced understanding of decay behavior in quasi-geostrophic equations

## Abstract

The initial value problem for the two dimensional dissipative quasi-geostrophic equation of the critical and the supercritical cases is considered. Anomalous diffusion on this equation provides slow decay of solutions as the spatial parameter tends to infinity. In this paper, uniform estimates for far field asymptotics of solutions are given.