Global Well-Posedness and Persistence of H2 Regularity for the Three-Dimensional Primitive Equations with Horizontal and Topography-Adapted Thermal Diffusion
Abstract
We study the three-dimensional primitive equations with full viscosity and horizontal thermal diffusion in bounded domains. We establish global well-posedness for admissible H1 initial data and persistence of H2 regularity on the flat-bottom cylinder. The higher regularity analysis combines fractional hydrostatic Stokes regularity with anisotropic estimates of the vertical transport. We also consider variable-depth domains with positive h∈ C3(M̅) and a diffusion operator adapted to the topography compatible with layers z/h(x,y)=constant. This operator reduces to ΔH at constant depth and generally differs from the Cartesian horizontal Laplacian over a varying bottom. Its weighted formulation yields global strong solutions for admissible H1 data. Persistence of H2 regularity is proved under the additional assumption ∂νh=0 on ∂ M, where ν is the outward horizontal unit normal.
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BibTeX
@misc{wang2026global,
title = {{Global Well-Posedness and Persistence of H2 Regularity for the Three-Dimensional Primitive Equations with Horizontal and Topography-Adapted Thermal Diffusion}},
author = {Qimin Wang and Mohammed Ziane},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14555},
eprint = {2610.14555},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14555},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global Well-Posedness and Persistence of H2 Regularity for the Three-Dimensional Primitive Equations with Horizontal and Topography-Adapted Thermal Diffusion
AU - Qimin Wang
AU - Mohammed Ziane
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14555
UR - https://arxiv.org/abs/2610.14555
AB - We study the three-dimensional primitive equations with full viscosity and horizontal thermal diffusion in bounded domains. We establish global well-posedness for admissible H^1 initial data and persistence of H^2 regularity on the flat-bottom cylinder. The higher regularity analysis combines fractional hydrostatic Stokes regularity with anisotropic estimates of the vertical transport. We also consider variable-depth domains with positive h∈ C^3(M̅) and a diffusion operator adapted to the topography compatible with layers z/h(x,y)=constant. This operator reduces to Δ_H at constant depth and generally differs from the Cartesian horizontal Laplacian over a varying bottom. Its weighted formulation yields global strong solutions for admissible H^1 data. Persistence of H^2 regularity is proved under the additional assumption ∂_νh=0 on ∂ M, where ν is the outward horizontal unit normal.
ER -