Global well-posedness of the 2D primitive equations with fractional horizontal dissipation

TL;DR

This paper proves the global existence and uniqueness of strong solutions for the 2D primitive equations with fractional horizontal dissipation, depending on the dissipation exponent and initial data size.

Contribution

It establishes the global well-posedness of strong solutions for the 2D primitive equations with fractional dissipation for a range of dissipation exponents and initial data conditions.

Findings

Global well-posedness for $\alpha \geq\alpha_0$ with large initial data.

Global well-posedness for $\alpha ext{ in } [1, \alpha_0)$ with small initial data.

Smallness condition only on the $L^\infty$ norm of initial vorticity.

Abstract

In this paper, we investigate the two-dimensional incompressible primitive equations with fractional horizontal dissipation. Specifically, we establish global well-posedness of strong solutions for arbitrarily large initial data when the dissipation exponent satisfies $\alpha\geq\alpha_{0}\approx1.1108$. In addition, we prove global well-posedness of strong solutions for small initial data when $\alpha \in [1, \alpha_0)$. Notably, the smallness assumption is imposed only on the $L^\infty$ norm of the initial vorticity.