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

Changhui Tan; Zhuan Ye

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arXiv · 2511.02723

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

Changhui Tan·Zhuan Ye

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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.

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Changhui Tan, Zhuan Ye. 2025-11-04. Global well-posedness of the 2D primitive equations with fractional horizontal dissipation. https://arxiv.org/abs/2511.02723

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