THE STOCHASTIC PRIMITIVE EQUATIONS WITH NONISOTHERMAL TURBULENT PRESSURE

• 成果类型: Article
• 署名作者: Agresti, Antonio; Hieber, Matthias; Hussein, Amru; Saal, Martin
• 署名单位: Institute of Science & Technology - Austria; Technical University of Darmstadt; University of Kaiserslautern
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2124
• 发表日期: 2025
• 页码: 635-700
• 关键词: navier-stokes equations; well-posedness; hydrostatic approximation; rigorous justification; ocean; atmosphere; REGULARITY; EXISTENCE; SYSTEM

摘要

In this paper, we introduce and study the primitive equations with non- isothermal turbulent pressure and transport noise. They are derived from the Navier-Stokes equations by employing stochastic versions of the Boussinesq and the hydrostatic approximations. The temperature dependence of the turbulent pressure can be seen as a consequence of an additive noise acting on the small vertical dynamics. For such a model we prove global well-posedness in H1 where the noise is considered in both the It & ocirc; and Stratonovich formulations. Compared to previous variants of the primitive equations, the one considered here presents a more intricate coupling between the velocity field and the temperature. The corresponding analysis is seriously more involved than in the deterministic setting. Finally, the continuous dependence on the initial data and the energy estimates proven here are new, even in the case of isothermal turbulent pressure.