Mathematical Open Problems of the Navier-Stokes Equations
纳维-斯托克斯方程的数学开放问题
基本信息
- 批准号:09304023
- 负责人:
- 金额:$ 13.57万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (A)
- 财政年份:1997
- 资助国家:日本
- 起止时间:1997 至 1998
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Progress is made in the study of the Navier-Stokes equation, the Burgers equations, and the reaction-diffusion equations. Okamoto and Shoji performed numerical experiments on the bifurcation of surface waves. New bifurcation diagrams are found and will be published in a form of textbook by World Scientific Inc. Okamoto and Sakajo compute numerically two-dimensional and three-dimensional vortex sheet motion. T.Ikeda and H.Ikeda consider a certain system of reaction-diffusion equations for three competing species. They clarify the structure of steady-states and traveling pulses. Their stability is also determined. K.Ohkitani and M.Yamada consider what is called the shell model of the turbulence. By numerical methods, they compute the Lyapunov numbers of the system and they study the scaling properties of the numbers. They derive an asymptotic formula as the viscosity tends to zero. T.Nakaki consider the motion of vortex patches as well as point vortices. He finds that the motion of the patches are quite similar to that of point vortices if the size of the patches are small enough and that the motion of vortex patches are substantially different if the sizes are large. Y.Kimura considers the motion of point vortices on two-dimensional hyperbolic surfaces. Its Hamiltonian formalism are derived and the algebraic properties of the invariants are studied. T.Nishida numerically computes the Boussinesq equations, which are the master equations for the thermal convection. In particular he obtains numerically the bifurcation from the trivial solution to the stationary convective flow. He applies the numerical verification technique and derives new criteria.
Navier-Stokes方程、Burgers方程和反应扩散方程的研究取得了进展。Okamoto和Shoji对表面波的分叉进行了数值实验。发现了新的分叉图,并将由世界科学公司以教科书的形式出版。Okamoto和Sakajo数值计算了二维和三维涡面运动。T.Ikeda和H.Ikeda考虑了一类三种群竞争的反应扩散方程组。它们阐明了稳态和行进脉冲的结构。它的稳定性也是确定的。K.Ohkitani和M.Yamada考虑所谓的湍流壳模型。通过数值方法,他们计算系统的李雅普诺夫数,并研究了这些数的标度特性。他们导出了当粘性趋于零时的渐近公式。T.Nakaki考虑了涡斑和点涡的运动。他发现,如果斑块的尺寸足够小,斑块的运动与点涡的运动非常相似,而如果斑块的尺寸很大,涡斑的运动则有很大的不同。木村认为运动的点涡二维双曲曲面。导出了它的哈密顿形式,并研究了其不变量的代数性质。T.Nishida数值计算Boussinesq方程,这是热对流的主方程。特别是他获得数值分岔平凡的解决方案,以固定的对流。他应用数值验证技术并推导出新的准则。
项目成果
期刊论文数量(30)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
H.Okamoto: "Exact solutions of the Navier-Stokes equations via Leray's scheme" Japan J.Indus.Appl.Math.14. 169-197 (1997)
H.Okamoto:“通过 Leray 方案精确求解纳维-斯托克斯方程”Japan J.Indus.Appl.Math.14。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
M.Yamada: "Asymptotic formulae for the Lyapunov spectrum of fully-developed shell model turbulence" Phys.Rev.E.に掲載予定.
M.Yamada:“完全发展的壳模型湍流的李亚普诺夫谱的渐近公式” 计划发表在 Phys.Rev.E 上。
- DOI:
- 发表时间:
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- 影响因子:0
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- 通讯作者:
T.-P.Liu, A.Matsumura, and K.Nishihara: "Behaviors of solutions for the Burgers equation with boundary corresponding to rar-efaction waves" SIAM J.Math.Anal.29. 293-308 (1998)
T.-P.Liu、A.Matsumura 和 K.Nishihara:“边界对应于稀疏波的 Burgers 方程解的行为”SIAM J.Math.Anal.29。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
H.Okamoto: "Exact solutions of the Navier-Stokes equations via Leray's scheme" Japan Journal of Industrial and Applied Mathematics. vol.14. 169-197 (1997)
H.Okamoto:“通过 Leray 方案精确求解纳维-斯托克斯方程”,《日本工业与应用数学杂志》。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
H.Ikeda and T.Ikeda: "Bifurcation phenomena from standing pulse solutions in some reaction-diffusion systems" J.Dynamics and Differential Equations. to appear. (1999)
H.Ikeda 和 T.Ikeda:“某些反应扩散系统中驻留脉冲解的分岔现象”J.Dynamics and Differential Equations。
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- 影响因子:0
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OKAMOTO Hisashi其他文献
OKAMOTO Hisashi的其他文献
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{{ truncateString('OKAMOTO Hisashi', 18)}}的其他基金
Applied Analysis on the Navier-Stokes Equations and Related Dynamical Systems
纳维-斯托克斯方程及相关动力系统的应用分析
- 批准号:
20244006 - 财政年份:2008
- 资助金额:
$ 13.57万 - 项目类别:
Grant-in-Aid for Scientific Research (A)
A Study of Blow-up Problems and Singular Perturbation Problems arisingin Mathematical Fluid Mechanics
数学流体力学中的爆炸问题和奇异摄动问题的研究
- 批准号:
17204008 - 财政年份:2005
- 资助金额:
$ 13.57万 - 项目类别:
Grant-in-Aid for Scientific Research (A)
Applications of the dynamical systems theory and the singularity theory to mathematical fluid mechanics
动力系统理论和奇点理论在数学流体力学中的应用
- 批准号:
14204007 - 财政年份:2002
- 资助金额:
$ 13.57万 - 项目类别:
Grant-in-Aid for Scientific Research (A)
Application of the double exponential transform to integral transformations
双指数变换在积分变换中的应用
- 批准号:
11554002 - 财政年份:1999
- 资助金额:
$ 13.57万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Studies on singular perturbation problems in nonlinear mechanics
非线性力学奇异摄动问题的研究
- 批准号:
11304005 - 财政年份:1999
- 资助金额:
$ 13.57万 - 项目类别:
Grant-in-Aid for Scientific Research (A)
On the research and development of fast solvers arising in scientific computation
科学计算中快速求解器的研究与开发
- 批准号:
09554003 - 财政年份:1997
- 资助金额:
$ 13.57万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Mathematical analysis and numerical computation of nonlinear partial differential equations
非线性偏微分方程的数学分析与数值计算
- 批准号:
08454028 - 财政年份:1996
- 资助金额:
$ 13.57万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Studies on mathematical analysis and numerical computation of the Nevier-Stokes equations
内维-斯托克斯方程的数学分析与数值计算研究
- 批准号:
07304019 - 财政年份:1995
- 资助金额:
$ 13.57万 - 项目类别:
Grant-in-Aid for Scientific Research (A)