Higher-order regularity of solutions to the large scale moist atmosphere system

TL;DR

This paper investigates the higher-order regularity of solutions to the large scale moist atmosphere system, establishing well-posedness in H^2 space by enhancing vertical and horizontal regularity of solutions.

Contribution

It introduces an improved regularity framework for solutions, extending well-posedness results to higher-order Sobolev spaces for the moist atmosphere system.

Findings

Solutions exhibit higher-order regularity in vertical and horizontal directions.

Well-posedness of solutions in H^2 space is established.

Enhanced regularity results contribute to the mathematical understanding of atmospheric models.

Abstract

In this paper, we study the higher-order regularity of solutions to the large scale moist atmosphere system through the way of $p$-strong solutions. On the basis of the well-posedness results of strong solutions, we first improve the regularity of solutions in the vertical direction, and then improve the regularity in the horizontal direction. Thus we obtain the well-posedness of solutions in $H^{2}$ space.