论文标题
Korteweg类型的一维等温压缩流体的耗散结构
Dissipative structure of one-dimensional isothermal compressible fluids of Korteweg type
论文作者
论文摘要
本文研究了一个在一个空间维度中介绍可压缩，等温，粘性毛细血管流体的方程系统的耗散结构。结果表明，该系统满足了汉弗莱斯的真正耦合条件（J.双曲线不同，等等2，2005，第4、963-974号），这反过来又是扩展到Kawashima and Shizuta和Shizuta的经典状况高阶系统的扩展。 2，249-275）用于二阶系统。事实证明，真正的耦合意味着在恒定平衡状态周围线性化系统的溶液衰减。为此，使用傅立叶符号的对称性来构建适当的补偿矩阵。这些线性衰减估计意味着通过标准延续论证，将扰动对恒定平衡状态作为对完整非线性系统的解决方案的全球衰减。
This paper studies the dissipative structure of the system of equations that describes the motion of a compressible, isothermal, viscous-capillar fluid of Korteweg type in one space dimension. It is shown that the system satisfies the genuine coupling condition of Humpherys (J. Hyperbolic Differ. Equ. 2, 2005, no. 4, 963-974), which is, in turn, an extension to higher order systems of the classical condition by Kawashima and Shizuta (Tohoku Math. J. 40, 1988, no. 3, 449-464; Hokkaido Math. J. 14, 1985, no. 2, 249-275) for second order systems. It is proved that genuine coupling implies the decay of solutions to the linearized system around a constant equilibrium state. For that purpose, the symmetrizability of the Fourier symbol is used in order to construct an appropriate compensating matrix. These linear decay estimates imply the global decay of perturbations to constant equilibrium states as solutions to the full nonlinear system, via a standard continuation argument.
