# Uniform pointwise asymptotics of solutions to quasi-geostrophic equation

## TL;DR

This paper derives uniform pointwise asymptotics and estimates for solutions to the subcritical quasi-geostrophic equation, including derivatives, based on initial data in specific Lebesgue spaces, advancing understanding of solution behavior.

## Contribution

It provides the first two-sided pointwise estimates and uniform asymptotics for solutions and their derivatives of the subcritical quasi-geostrophic equation.

## Key findings

- Established two-sided pointwise estimates for solutions.
- Derived uniform asymptotics for solutions.
- Extended results to derivatives of solutions.

## Abstract

We provide two-sided pointwise estimates and uniform asymptotics of the solutions to the subcritical quasi-geostrophic equation with initial data in $L^{2/(\alpha-1)}(\mathbb{R}^2)$. Furthermore, we give upper bound of similar type for any derivative of the solutions. Initial data in $L^{p}(\mathbb{R}^2)$, $p>2/(\alpha-1)$, are also discussed.