论文标题
具有非等温湍流压力的随机原始方程
The stochastic primitive equations with non-isothermal turbulent pressure
论文作者
论文摘要
在本文中，我们以$ \ textit {non} $ - 等温湍流压力和运输噪声介绍和研究原始方程。它们是通过使用BoussinesQ和静水近似的随机版本来源自Navier-Stokes方程的。湍流压力的温度依赖性可以看见是由作用在小垂直动力学上的添加噪声的结果。对于这样的模型，我们证明了$ h^1 $中的全球体系良好，其中在ITô和Stratonovich配方中都考虑了噪声。与原始方程的先前变体相比，此处考虑的一个方程式在速度场和温度之间提出了更复杂的耦合。相应的分析比确定性设置更严重。最后，即使在等温湍流压力的情况下，此处证明的对初始数据和能量估计的持续依赖性也是新的。
In this paper, we introduce and study the primitive equations with $\textit{non}$-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 $H^1$ where the noise is considered in both the Itô 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.
