arXiv Preprint 2510.18759.
Tuesday, 04 November 2025 11:50
Global well-posedness of the 2D primitive equations with fractional horizontal dissipation
Changhui Tan, Zhuan Ye
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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This work is supported by NSF grants DMS #2238219 |
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