Asymptotic analysis of systems of nonlinear partial differential equations describing motions of viscous fluids

描述粘性流体运动的非线性偏微分方程组的渐近分析

• 批准号: 19340033
• 负责人: KAGEI Yoshiyuki
• 金额: $ 4.33万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19340033/
• 关键词: 圧縮性Navier-Stokes方程式; 安定性; 漸近挙動

We studied the asymptotic behavior of solutions of the compressible Navier-Stokes equation which describes motion of viscous fluids. We analyzed the stability properties of stationary solutions such as the motionless state and parallel flows in detail. It was proved that these stationary solutions are asymptotically stable if they are small enough in some sense. Furthermore, it was shown that the disturbances behave like solutions of convective heat equations in large time.

研究了描述粘性流体运动的可压缩Navier-Stokes方程解的渐近性态。详细分析了定态解的稳定性，如定态解和平行流解。证明了当这些平稳解在一定意义下足够小时，它们是渐近稳定的。此外，它表明，扰动的行为类似于对流热方程的大时间的解决方案。

项目成果

Asymptotic stability of stationary waves for viscous heat-conductive gases in half line

半线粘性导热气体驻波的渐近稳定性

• 发表时间: 2009
• 作者: 平原靖大;平尾強司;畳谷仁男;米津朋尚;岡知路;海老塚昇;川口建太郎;所仁志;T. Nakamura
• 通讯作者: T. Nakamura

Decay structure for systems of viscoelasticity, Mathematical Analysis on the Navier-Stokes Equatins and Related Topics

粘弹性系统的衰变结构、纳维-斯托克斯等号线的数学分析及相关主题

• 发表时间: 2009
• 作者: Yoshishige Haraoka;Galina Filipuk;S. Kawashima
• 通讯作者: S. Kawashima

Weighted estimates for the Stokes semigroup in an exterior domain

外部域中斯托克斯半群的加权估计

• 发表时间: 2008
• 作者: H. Aikawa;T. Kilpelainen;N. Shanmugalingam;and X. Zhong;Hiroshi Yanagihara;Takayuki KOBAYASHI;Yoichi Imayoshi;諸澤俊介;T. Ono;Hiroshi Yanagihara;Kenichi Sakan;諸澤俊介;T. Kobayashi;山田陽;Hiroaki Aikawa;山田 陽;諸澤俊介;Takayuki KOBAYASHI
• 通讯作者: Takayuki KOBAYASHI

On the existence of Burgers vortices for high Reynolds numbers

高雷诺数下伯格斯涡旋的存在性

• 发表时间: 2009
• 期刊: Journalof Mathematical Analysis and Applications 349
• 作者: Maekawa;Y
• 通讯作者: Y

Asymptotic Stability of Rarefaction Wave for the Navier–Stokes Equations for a Compressible Fluid in the Half Space

• DOI: 10.1007/s00205-008-0191-8
• 发表时间: 2009-08
• 期刊: Archive for Rational Mechanics and Analysis
• 影响因子: 2.5
• 作者: S. Kawashima;P. Zhu