Regularity of global solution to atmospheric circulation equations with humidity effect

Hong Luo

doi:10.1186/1687-2770-2012-143

Abstract

In this article, the regularity of the global solutions to atmospheric circulation equations with humidity effect is considered. Firstly, the formula of the global solutions is obtained by using the theory of linear operator semigroups. Secondly, the regularity of the global solutions to atmospheric circulation equations is presented by using mathematical induction and regularity estimates for the linear semigroups. MSC:35D35, 35K20, 35Q35.

Highlights

1 Introduction This paper is concerned with the regularity of solutions to the following initial-boundary problem of atmospheric circulation equations involving unknown functions (u, T, q, p) at (x, t) = (x, x, t) ∈ × (, ∞) ( = (, π ) × (, ) is a period of C∞ field (–∞, +∞) × (, )):
We deduce atmospheric circulation models which are able to show the features of atmospheric circulation and are easy to be studied from the very complex atmospheric circulation model based on the actual background and meteorological data, and we present global solutions of atmospheric circulation equations with the use of the T-weakly continuous operator [ ]
We investigate the regularity of the solutions to atmospheric circulation equations ( . )-( . )

Summary

Introduction

This paper is concerned with the regularity of solutions to the following initial-boundary problem of atmospheric circulation equations involving unknown functions (u, T, q, p) at (x, t) = (x , x , t) ∈ × ( , ∞) ( = ( , π ) × ( , ) is a period of C∞ field (–∞, +∞) × ( , )):. The atmosphere or the ocean or the couple atmosphere and ocean can be viewed as initial and boundary value problems [ – ], or an infinite dimensional dynamical system [ – ]. In [ ], the steady state solutions to atmospheric circulation equations with humidity effect are studied. In Section , we present the formula of the solution to the atmospheric circulation equations. In Section , we obtain the regularity of the solutions to equations · X denotes the norm of the space X, and C, Ci are variable constants

Preliminaries We consider the divergence form of the linear elliptic equation

Formula of global solutions We introduce the spaces