# Sharp constant of an anisotropic Gagliardo-Nirenberg-type inequality and applications

## TL;DR

This paper determines the optimal constant for a specific anisotropic Gagliardo-Nirenberg inequality related to the Benjamin-Ono-Zakharov-Kuznetsov equation and applies it to establish uniform bounds for solutions in the energy space.

## Contribution

It provides the exact best constant for an anisotropic Gagliardo-Nirenberg inequality and demonstrates its application to solution bounds for a related PDE.

## Key findings

- Established the best constant for the anisotropic Gagliardo-Nirenberg inequality.
- Proved uniform bounds of solutions in the energy space for the Benjamin-Ono-Zakharov-Kuznetsov equation.

## Abstract

In this paper we establish the best constant of an anisotropic Gagliardo-Nirenberg-type inequality related to the Benjamin-Ono-Zakharov-Kuznetsov equation. As an application of our results, we prove the uniform bound of solutions for such a equation in the energy space.