Real analytic approach to the stability theory of nonlinear evolution equations

非线性演化方程稳定性理论的实解析方法

• 批准号: 12440045
• 负责人: SHIBATA Yoshihiro
• 金额: $ 9.34万
• 依托单位: Waseda University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-12440045/
• 关键词: Oseen equation; Flew in the infinite layer; Stokes operator; Stability of the flew; Resolvent problem; Incompressible viscous fluid flow; Compressible viscous fluid flow; Free boundary value problem; 数学; 基礎解析; n-dim. Navier-Stokes equation; Sta

1.Stability of the Oseen flow in the n-dimensional exterior domain (n>2).2.Stability of the Couette flow and the Poiseuille flow in the infinite layer.3.Rate of convergence of the non-stationary flow to the stationary flow of compressible viscous fluid.4.Resolvent estimate of solutions to the Stokes equation with Neumann boundary condition.

1.Oseen流在n维外域的稳定性（n>2）。库埃特流和泊泽维尔流在无限层中的稳定性。可压缩粘性流体的非定常流向定常流的收敛速度。具有Neumann边界条件的Stokes方程解的可解估计。

项目成果

V.Shibata, S.Shimizu: "On a resolvent estimate of the literface problem for the Stokes system in a bounded domain"J.Diff.Eqns.. 191. 408-444 (2003)

V.Shibata、S.Shimizu：“关于有界域中 Stokes 系统的字面问题的解析估计”J.Diff.Eqns.. 191. 408-444 (2003)

P.Secchi, Y.Shibata: "On the decay of solutions to the 2D Neumann exterior problem for the wave equation"Journal of Differential Equations. 194. 221-236 (2003)

P.Secchi、Y.Shibata：“关于波动方程的二维诺依曼外问题解的衰减”微分方程杂志。

Y.Shibata: "Time-global solutions of nonlinear evolution equations and their stability"American Mathematical Society, Translations. 211. 87-105 (2003)

Y.Shibata：“非线性演化方程的时间全局解及其稳定性”美国数学会，译着。

Y.Shibata, S.Shimizu: "On a resolvent estimate of the interface problem for the Stokes system in abouded domain"J. Diff. Eqns.. 191. 408-444 (2003)

Y.Shibata，S.Shimizu：“关于在丰富域中斯托克斯系统的界面问题的解析估计”J。

Y.Shibata: "On the rate of decay of solutions to linear viscoelastic equation"Math. Meth. Appl. Sci.. 23. 203-226 (2000)

Y.Shibata：“关于线性粘弹性方程解的衰减率”数学。