Regularity results for the Primitive Equations of the ocean

TL;DR

This paper derives regularity results for the linear Primitive Equations of the ocean, explicitly calculating the pressure term and establishing existence and uniqueness under low-regularity conditions.

Contribution

It provides explicit pressure calculations and new regularity results for the linear Primitive Equations with low-regularity data.

Findings

Explicit pressure term calculation via Fourier transforms.

Existence and uniqueness results for low-regularity right-hand sides.

Regularity properties of solutions to the linear Primitive Equations.

Abstract

We consider the linear Primitive Equations of the ocean in the three dimensional space, with horizontal periodic and vertical Dirichlet boundary conditions. Thanks to Fourier transforms we are able to calculate explicitly the pressure term. We then state existence, unicity and regularity results for the linear time-depending Primitive Equations, with low-regularity right-hand side.