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

KDV方程和Kawahara方程是从表面波正式得出的，如长波近似。在以适当的非二维形式重写方程后，我们有两个非二维参数δ和ε分别是水深度与波长的比率和自由表面的放大器与水深度的比率。极限δ→0对应于长波近似。更确切地说，极限δ=ε^2→0对应于KDV极限，而极限δ=ε^4→0对应于Kawahara限制。 T.iguchi在数学上对KDV和Kawahara限制给出了严格的理由，并证明了这些近似方程的解决方案实际上近似于原始基本方程的解决方案，以适用于适当的长时间间隔。他还分析了这些长波近似底部不均匀的影响。他发现了溶液的组对称性与溶液的时空衰减特性之间的关系。他还调查了欧拉方程的二维不可压缩理想的理想流体占据了一个外部领域，并发现了压力的平方整合与流向障碍物的效果之间的关系。他证明，在适当的初始数据和外部力的假设下，固定溶液在不对称上是不对称的。他没有假设数据的任何较小条件。他发现了线性化问题的一个不错的解决方案。通过使用公式并非常仔细地对振荡性积分进行分析，他获得了最佳的衰减估计值，并证明了不对称的稳定性。较少的