Global existence and large time behavior for primitive equations with free boundary

TL;DR

This paper proves the global existence, uniqueness, and long-term behavior of solutions to primitive equations with free boundaries, relevant for modeling ocean and atmosphere dynamics.

Contribution

It establishes the first rigorous results on global solutions and their asymptotic convergence for primitive equations with free moving boundaries.

Findings

Global existence and uniqueness of strong solutions.

Exponential convergence to equilibrium in periodic domains.

Algebraic convergence in whole space domains.

Abstract

In the present paper, the primitive equations, which can be used to simulate the large scale motion of ocean and atmosphere, are considered in the three-dimensional domain bounded below by a fixed solid boundary and above by a free moving boundary. The global existence and uniqueness of strong solutions are established and the long time convergence to the equilibrium state is showed either at exponential rate for horizontal periodic domain or at algebraic rate for horizontal whole space.