The stability about Navier-Stokes equation and Euler equation was brought into comparison. And by taking their typical initial value problem for example, the reason of leading to the difference in stability between Na...The stability about Navier-Stokes equation and Euler equation was brought into comparison. And by taking their typical initial value problem for example, the reason of leading to the difference in stability between Navier-Stokes equation and Euler equation was also analyzed.展开更多
Based on the theory of stratification, the well-posedness of the initial value problem for the linear shallow-water equations on an equatorial beta-plane was discussed. The sufficient and necessary conditions of the e...Based on the theory of stratification, the well-posedness of the initial value problem for the linear shallow-water equations on an equatorial beta-plane was discussed. The sufficient and necessary conditions of the existence and uniqueness for the local solution of the equations were presented and the existence conditions for formal solutions of the equations vere also given. For the Cauchy problem on the hyper-plane {t = O}, the local analytic solution were worked out and a special case was discussed. Finally, an example was used to explain the variety of formal solutions for the ill-posed problem.展开更多
基金Project supported by the National Natural Science Foundation of China (Major Program of the Tenth Five-Year Plan) (No.90411006)
文摘The stability about Navier-Stokes equation and Euler equation was brought into comparison. And by taking their typical initial value problem for example, the reason of leading to the difference in stability between Navier-Stokes equation and Euler equation was also analyzed.
基金Project supported by the National Natural Science Foundation of China (Grant No: 90411006, 40175014) and the Key Foundation of Shanghai Municipal Commission of Science and Technology (Grant No: 02DJ14032)
文摘Based on the theory of stratification, the well-posedness of the initial value problem for the linear shallow-water equations on an equatorial beta-plane was discussed. The sufficient and necessary conditions of the existence and uniqueness for the local solution of the equations were presented and the existence conditions for formal solutions of the equations vere also given. For the Cauchy problem on the hyper-plane {t = O}, the local analytic solution were worked out and a special case was discussed. Finally, an example was used to explain the variety of formal solutions for the ill-posed problem.
