十大网投正规信誉官网黄春妍教授与合作者美国布朗大学的Yan Guo教授，Benoit Pausader教授、瑞士苏黎世大学的Klaus Widmayer教授在国际顶级数学期刊Communications on Pure and Applied Mathematics（简称CPAM）上发表了题为《On the stabilizing effect of rotation in the 3d Euler equations》的研究论文。该论文研究了常速度旋转对三维不可压欧拉方程的长时间非线性动力学效应，证明了对充分小的轴对称初值，解几乎整体存在稳定。这说明旋转会改善方程解的稳定性，且不需要考虑旋转的速度。

该问题的主要困难在于色散关系是各项异性且退化，衰减速度很慢不可积。本文开发了各向异性的研究框架，建立了多种对称性，精确量化和控制非线性相互作用，同时通过线性色散估计给出色散退化估计的充分信息。除了小初值和轴对称条件，没有对初值施加其它条件，且解可以有非零旋度。根据经典理论，带非零旋度的解先验只能存在很短时间，最近的一些结果说明不带旋转和轴对称的初值会导致解在有限时间形成奇性。此结果表明旋转会阻止充分光滑小解的奇性的形成。

CPAM期刊于1948年由享有盛名的美国柯朗数学科学研究所创刊，刊载纯粹数学、应用数学等领域有突破性和创新性的一流研究成果。

论文摘要：While it is well known that constant rotation induces linear dispersive effects in various fluid models, we study here its effect on long time nonlinear dynamics in the inviscid setting. More precisely, we investigate stability in the 3d rotating Euler equations in ℝ3 with a fixed speed of rotation. We show that for any M> 0, axisymmetric initial data of sufficiently small size lead to solutions that exist for a long time and disperse. This is a manifestation of the stabilizing effect of rotation, regardless of its speed. To achieve this we develop an anisotropic framework that naturally builds on the available symmetries. This allows for a precise quantification and control of the geometry of nonlinear interactions, while at the same time giving enough information to obtain dispersive decay via adapted linear dispersive estimates.

下载链接：https://doi.org/10.1002/cpa.22107

撰稿人：黄春妍

审稿人：邓露