Interaction of Deterministic or Stochastic Forces on Flat or Moving Interfaces

平面或移动界面上确定性或随机力的相互作用

• 批准号: 520471868
• 负责人: Professor Dr. Matthias Hieber
• 金额: --
• 依托单位: AG Analysis
• 依托单位国家: 德国
• 项目类别: Research Units
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/520471868?language=en
• 关键词: Interaction; Deterministic; Stochastic; Forces; Flat

This project concerns the interaction of geophysical flows with deterministic or stochastic forces on flat or moving boundaries. The evolution of a geophysical flow governed by the primitive equations in geometries with flat boundaries and homogeneous boundary data is rather well understood in the setting of Sobolev spaces as well as for continuous functions. In fact, the underlying equations are known to be strongly globally well-posed, when considered on fixed flat boundaries and without forces. This is no longer the case when deterministic or stochastic forces are applied or when the underlying domain is allowed to be a moving interface as in the case of moving or free boundary value problems. This project aims at a simultaneous advance in a deeper understanding of outer forces and moving interfaces by investigating four circles of problems: study the effects of stochastic forcing through transport noise, investigate wind driven boundary condition described by a Wiener process, construct strong solutions to associated free boundary value problems and study fluid-structure interaction or fluid-sea ice coupling within the deterministic setting. In more detail we shall: - study global existence results for non-isothermal primitive equations subject to transport noise, - investigate the free boundary value problem for the primitive equations, - examine global strong solutions for the primitive equations subject to stochastic wind driven boundary conditions and extend the setting to free surfaces, - consider coupled atmosphere-sea ice-ocean models with regard to global solutions and free interfaces, - investigate fluid-structure interactions for geophysical flows and ice structures such as icebergs. In contrast to the Navier-Stokes equations, the study of transport noise in the context of geophysical flows is a rather new field. The starting points are the stochastic counterparts of the classical Boussinesq and hydrostatic approximations. The question on the extension of the local pathwise solution to the primitive equations subject to stochastic wind driven boundary conditions to a global one will be investigated by energy estimates in Sobolev spaces of negative order. In the deterministic setting concerning free or moving interfaces we plan to transform the problems to sets of equations on fixed domains and apply recent decoupling methods. The analysis of the coupled atmosphere-sea ice-ocean model on flat or free interfaces will rely on these methods.

该项目涉及地球物理流与平坦或移动边界上的确定性或随机力的相互作用。在索博列夫空间以及连续函数的设置中，由具有平坦边界和齐次边界数据的几何中的原始方程控制的地球物理流的演化是相当容易理解的。事实上，当在固定的平坦边界上且没有力的情况下考虑时，基础方程被认为是强全局适定的。当应用确定性或随机力或者当底层域被允许是移动界面（如移动或自由边值问题的情况）时，情况不再是这样。该项目旨在通过研究四个问题来同时推进对外力和移动界面的更深入理解：研究传输噪声中的随机强迫的影响，研究维纳过程描述的风驱动边界条件，构建相关自由边值问题的强大解决方案，以及研究确定性环境中的流体-结构相互作用或流体-海冰耦合。更详细地说，我们将： - 研究受传输噪声影响的非等温基元方程的全局存在结果， - 研究基元方程的自由边值问题， - 检查受随机风驱动边界条件影响的基元方程的全局强解，并将设置扩展到自由表面， - 考虑关于全局解和自由界面的大气-海冰-海洋耦合模型， - 研究地球物理流的流体-结构相互作用，以及 冰山等冰结构。与纳维-斯托克斯方程相比，地球物理流背景下的传输噪声研究是一个相当新的领域。起点是经典 Boussinesq 和流体静力近似的随机对应点。将受随机风驱动边界条件影响的原方程的局部路径解扩展到全局方程的问题将通过负阶 Sobolev 空间中的能量估计来研究。在涉及自由或移动界面的确定性设置中，我们计划将问题转化为固定域上的方程组，并应用最新的解耦方法。平坦或自由界面上大气-海冰-海洋耦合模型的分析将依赖于这些方法。