论文标题
旋转分层的Boussinesq系统的近谐振近似在3多头
Near Resonant Approximation of the Rotating Stratified Boussinesq system on a 3-Torus
论文作者
论文摘要
基于对近共振的新型处理，我们在三维tori上引入了新的旋转分层的Boussinesq系统，该近似值具有任意纵横比。旋转和分层参数是任意的，不相等。我们为任意大的初始数据获得了建议的非线性系统的全局存在。该系统足够准确，具有慢速和快速模式之间耦合效果的重要特征。全球存在的关键是对非线性相互作用数量的急剧计数。仔细检查一些混合类型的相互作用系数引起了额外的规律性优势。在更广泛的背景下，与基于精确的共鸣相比，我们近乎共鸣的方法的重要性是包含更多相互作用模式与改善规律性属性之间的微妙平衡。
Based on a novel treatment of near resonances, we introduce a new approximation for the rotating stratified Boussinesq system on three-dimensional tori with arbitrary aspect ratios. The rotation and stratification parameters are arbitrary and not equal. We obtain global existence for the proposed nonlinear system for arbitrarily large initial data. This system is sufficiently accurate, with an important feature of coupling effects between slow and fast modes. The key to global existence is a sharp counting of the relevant number of nonlinear interactions. An additional regularity advantage arises from a careful examination of some mixed type interaction coefficients. In a wider context, the significance of our near resonant approach is a delicate balance between the inclusion of more interacting modes and the improvement of regularity properties, compared to the well-studied singular limit approach based on exact resonance.
