Continuous Dependence on the Heat Source of 2D Large-Scale Primitive Equations in Oceanic Dynamics

Yuanfei Li,Peng Zeng

doi:10.3390/sym13101961

Abstract

In this paper, we consider the initial-boundary value problem for the two-dimensional primitive equations of the large-scale oceanic dynamics. These models are often used to predict weather and climate change. Using the differential inequality technique, rigorous a priori bounds of solutions and the continuous dependence on the heat source are established. We show the application of symmetry in mathematical inequalities in practice.

Highlights

Primitive equations are very useful models which are often used to study the climate and weather prediction
Assuming that all unknown functions are independent of the latitude y, Petcu et al [5] obtained the two-dimensional primitive equations of the ocean from the three-dimensional primitive equations
Huang et al [7] studied the two-dimensional primitive equations of large-scale ocean in geophysics driven by degenerate noise

Summary

Introduction

Primitive equations are very useful models which are often used to study the climate and weather prediction. Huang and Guo [6] considered the two-dimensional primitive equations of large-scale oceanic motion. They obtained the the existence and uniqueness of global strong solutions. The aim of this paper is to prove the continuous dependence on the heat source of problem (1)–(3) by using the energy methods. This type of study is devoted to know whether a small change in the equation can cause a large change in the solutions.

Preliminaries of the Problem

Conclusions