论文标题
位置不确定性下的随机旋转浅水模型的分析特性
Analytical Properties for a Stochastic Rotating Shallow Water Model under Location Uncertainty
论文作者
论文摘要
旋转的浅水模型是对海洋和大气一般循环模型的简化，这些模型用于许多应用，例如潮流预测，海啸跟踪和海洋建模。在本文中，我们介绍了一类旋转的浅水模型，这些模型在随机上受到干扰，以将模型不确定性纳入基础系统。正如[Mémin，2014年]所介绍的那样，通过遵循位置不确定性原则来选择随机性。我们证明，所得方程是具有独特最大强溶液的一类随机部分微分方程的一部分。该方法是基于在适当选择的有限维木材 - 小木制空间中构建具有值的近似模型序列。最后，我们表明，这类随机部分微分方程的杰出要素具有全球弱解。
The rotating shallow water model is a simplification of oceanic and atmospheric general circulation models that are used in many applications such as surge prediction, tsunami tracking and ocean modelling. In this paper we introduce a class of rotating shallow water models which are stochastically perturbed in order to incorporate model uncertainty into the underlying system. The stochasticity is chosen in a judicious way, by following the principles of location uncertainty, as introduced in [Mémin, 2014]. We prove that the resulting equation is part of a class of stochastic partial differential equations that have unique maximal strong solutions. The methodology is based on the construction of an approximating sequence of models taking value in an appropriately chosen finite-dimensional Littlewood-Paley space. Finally, we show that a distinguished element of this class of stochastic partial differential equations has a global weak solution.
