Study on the change of patterns of vortices and waves in fluid flow.

流体流动中涡波模式变化的研究。

• 批准号: 15340054
• 负责人: MIYAKAWA Tetsuro
• 金额: $ 9.79万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15340054/
• 关键词: Navier-Stokes equations; Initial value problem; Free surface; Group-symmetry; Stability; Vortex filament; Vortex ring; Singular integral; パターン形成; 対称性; 水面波; 漸近挙動; Navier-Stokes方程式; 自由境界問題; 漸近形; パターン形式

MIYAKAWA studied the flows of a viscous incompressible fluid in two and three-dimensional exterior domains and clarified explicit relationship between the space-time decay rates of flows and the symmetry of solutions of the equations of motion. He obtained almost complete results in the case of two space dimensions. FUKUMOTO studied the evolution of viscous vortices, applying the singular perturbation method to the non-local induction model, and obtained new results on the topological change of vortex filaments and rings. HISHIDA studied the viscous flow around a rotating body and proved for the first time the existence of stationary and nonstationary flows by finding a new class of singular integral operators. He also gave a new existence result for flows in domains with apertures. IGUCHI applied the method for treating free-surface problem to the equation of one-dimensional gas dymanics and gave a completely new approach to this problem which has wide applications to equations of similar types. He also classified the shape of free surfaces associated with shallow water flow with periodic bottom, applying the bifurcation theory.

Miyakawa研究了粘性不可压缩流体在二维和三维外部区域中的流动，阐明了流动的时空衰减率与运动方程解的对称性之间的显式关系。他获得了几乎完整的结果的情况下，两个空间维度。FUKUMOTO将奇异摄动方法应用于非定域诱导模型，研究了粘性涡的演化，得到了涡丝和涡环拓扑变化的新结果。HISHIDA研究了旋转体周围的粘性流动，并通过寻找一类新的奇异积分算子首次证明了定常和非定常流动的存在性。他还给出了一个新的存在性结果流域与孔。IGUCHI将自由面问题的处理方法应用于一维气体动力学方程，给出了一种全新的求解方法，对类似类型的方程有着广泛的应用。他还分类形状的自由表面与浅水流动周期性的底部，应用分叉理论。

项目成果

A Mathematical justification of the forced Korteweg-de Vries equation

强制Korteweg-de Vries方程的数学论证

• 期刊: Kyushu Journal of Mathematic (掲載予定)
• 作者: Tatsuo Iguchi

井口達雄: "Existence theory for hyperbolic systems of conservation laws with general flux-functions"Archives for Rational Mechanics and Analysis. 168. 165-244 (2003)

Tatsuo Iguchi：“具有一般通量函数的守恒定律双曲系统的存在理论”理性力学与分析档案 168. 165-244 (2003)。

Short-wavelength stability analysis of thin vortex rings

• DOI: 10.1063/1.1606446
• 发表时间: 2003-09
• 期刊: Physics of Fluids
• 影响因子: 4.6
• 作者: Y. Hattori;Y. Fukumoto

Conservation laws of circulation and helicity as Noether's theorem.

循环和螺旋守恒定律如诺特定理。

• 发表时间: 2004
• 期刊: Computational Fluid Dynamics Journal 13
• 作者: P.Polacik;E.Yanagida;Yasuhide FUKUMOTO
• 通讯作者: Yasuhide FUKUMOTO

He Cheng: "On L^1-summability and asymptotic profiles for smooth solutions to Navier-Stokes equations in a 3D exterior domain"Mathematische Zeitschrift. 245. 387-417 (2003)

何成：“关于 3D 外部域中纳维-斯托克斯方程平滑解的 L^1-可求性和渐近轮廓”Mathematische Zeitschrift。