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arXiv · 2607.27724

The primitive equations on curved surfaces

M. Hieber·Y. Shao·G. Simonett·M. Wilke
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Abstract

In this paper, we study the primitive equations in a collar neighborhood of a smooth closed hypersurface in ${\mathbb R}^3$. Using the framework of maximal $L_q$-regularity and the hydrostatic Helmholtz projection, we establish existence, uniqueness, and regularity results for strong solutions. Building on these local well-posedness results, we derive suitable a priori estimates and prove the global existence of strong solutions without imposing any smallness assumptions for the initial data. Moreover, we show that the solutions are $C^\infty$ jointly in time and space.

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M. Hieber, Y. Shao, G. Simonett, M. Wilke. 2026-07-30. The primitive equations on curved surfaces. https://arxiv.org/abs/2607.27724

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