The Temporal decay rate of solutions to 2D dissipative quasi-geostrophic flows

TL;DR

This paper establishes the algebraic decay rate of higher order derivatives for solutions to 2D dissipative quasi-geostrophic flows using Fourier splitting and decay character properties.

Contribution

It introduces a method to determine decay rates of higher order derivatives in 2D dissipative quasi-geostrophic equations, expanding understanding of solution behavior.

Findings

Derived algebraic decay rates for solutions

Applied Fourier splitting method effectively

Extended decay character properties to higher derivatives

Abstract

In this paper, by using Fourier splitting method and the expanded properties of decay character $r^*$, we establish the algebraic decay rate of higher order derivative of solutions to 2D dissipative quasi-geostrophic flows.