GLOBAL ESTIMATES AND BLOW-UP CRITERIA FOR THE GENERALIZED HUNTER-SAXTON SYSTEM
GLOBAL ESTIMATES AND BLOW-UP CRITERIA FOR THE GENERALIZED HUNTER-SAXTON SYSTEM
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DOI：
10.3934/dcdsb.2015.20.641
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发表时间：
2013-07
影响因子：
1.2
通讯作者：
Alejandro Sarria
中科院分区：
文献类型：
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作者：
Alejandro Sarria
广义的二元亨特-萨克斯顿系统包含几个众所周知的流体动力学模型，可作为研究一维流体对流和拉伸的工具。本文推导了系统周期解的一般表示公式，该公式对于参数 $(\lambda,\kappa) \in \mathbb{R} \times \mathbb{R}$ 的任意值都有效。这使我们能够详细检查爆炸的定性特性以及解的渐近行为，包括在有限或无限时间内收敛到稳态。
The generalized, two-component Hunter-Saxton system comprises several well-known models of fluid dynamics and serves as a tool for the study of one-dimensional fluid convection and stretching. In this article a general representation formula for periodic solutions to the system, which is valid for arbitrary values of parameters $(\lambda,\kappa) \in \mathbb{R} \times \mathbb{R}$, is derived. This allows us to examine in great detail qualitative properties of blow-up as well as the asymptotic behaviour of solutions, including convergence to steady states in finite or infinite time.