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On an analysis globally in time of solutions for surface waves

面波解的全局及时分析

基本信息

批准号：
15540200
负责人：
IGUCHI Tatsuo
金额：
$ 2.24万
依托单位：
Tokyo Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
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/en/grant/KAKENHI-PROJECT-15540200/
关键词：
surface wave KdV equation Kawahara equation forced KdV equation Navier-Stokes equations hyperbolic-parabolic system long wave approximation group symmetry Benjamin-Ono方程式表面張力 forced kdV方程式 kawahara方程式漸近挙動熱対流

项目摘要

The KdV equation and the Kawahara equation were derived formally from the basic equations for surface waves as long wave approximations. After rewriting the equations in an appropriate non-dimensional form, we have two non-dimensional parameters δ and ε the ratio of the water depth to the wave length and the ratio of the amplitude of the free surface to the water depth, respectively. The limit δ→0 corresponds to the long wave approximation. More precisely, the limit δ=ε^2→0 corresponds to the KdV limit and the limit δ=ε^4→0 corresponds to the Kawahara limit. T.Iguchi gave mathematically rigorous justifications for the KdV and the Kawahara limits and proved that the solutions of these approximate equations in fact approximate the solutions of the original basic equations for an appropriate long time interval. He also analyzed an effect of the presence of an uneven bottom to these long wave approximations.T.Miyakawa investigated the Navier-Stokes equations for a two-dimensional incompres … More sible viscous fluid in the cases where the fluid is occupied the entire space or outside of the unit disc. He discovered the relation between the group symmetries of the solution and the space-time decay properties of the solution. He also investigated the Euler equation for a two-dimensional incompressible ideal fluid occupied an exterior domain and discovered a relation between the square integrability of the pressure and the effect of the flow to the obstacle.S.Nishibata investigated the asymptotic behavior in time of the spherically symmetric solution for compressible Navier-Stokes equations in the exterior domain of the sphere. He proved that a stationary solution is asymptotically stable under suitable assumptions for the initial data and the external forces. He did not suppose any smallness conditions for the data.Y.Kagei investigated the asymptotic stability of a stationary solution for the compressible Navier-Stokes equations in the half-space. He discovered a nice solution formula to the linearized problem. By using the formula and carrying out the analysis very carefully for the oscillatory integrals, he obtained the best possible decay estimates and proved the asymptotic stability. Less

从表面波的基本方程出发，导出了长波近似的KdV方程和Kawahara方程。将方程改写成适当的无量纲形式后，得到两个无量纲参数δ和ε，分别为水深与波长的比值和自由表面振幅与水深的比值。极限δ→0对应于长波近似。更准确地说，极限δ=ε^2→0对应于KdV极限，极限δ=ε^4→0对应于川原极限。T.Iguchi对KdV和Kawahara极限给出了数学上严格的证明，并证明了这些近似方程的解实际上在适当的长时间间隔内近似于原始基本方程的解。他还分析了不均匀底部的存在对这些长波近似的影响。T.Miyakawa研究了二维非压缩的Navier-Stokes方程。 ...更多信息在流体占据单元盘的整个空间或外部的情况下，他发现之间的关系组对称性的解决方案和时空衰变性质的解决方案。他还研究了欧拉方程的二维不可压缩的理想流体占据了外部领域，并发现了一个关系的平方积分的压力和影响的流动的障碍。S.西巴塔调查的渐近行为在时间的球对称解决方案可压缩的Navier-Stokes方程的外部领域的领域。他证明了一个固定的解决方案是渐近稳定的适当假设下的初始数据和外力。他没有假设任何小条件的数据。Y.Kagei调查的渐近稳定性的固定解决方案的可压缩Navier-Stokes方程的半空间。他发现了线性化问题的一个很好的求解公式。通过使用公式和进行分析非常仔细的振荡积分，他获得了最好的可能衰减估计，并证明了渐近稳定。少