EXISTENCE AND REGULARITY OF SOLUTIONS AND THE STABILITY OF THE REST STATE FOR FLUIDS WITH SHEAR DEPENDENT VISCOSITY
EXISTENCE AND REGULARITY OF SOLUTIONS AND THE STABILITY OF THE REST STATE FOR FLUIDS WITH SHEAR DEPENDENT VISCOSITY
复制标题
剪切相关粘度流体解的存在性、规律性以及静止状态的稳定性
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
M. Růžička
中科院分区：
文献类型：
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作者：
J. Málek;K. Rajagopal;M. Růžička
在这篇文章中，我们澄清和讨论了Malek，Necas和RůžIk所考虑的非牛顿流体模型的一些微妙特征。19我们建立了关于这类非牛顿流体在任意初始扰动下机械孤立流动的休止态稳定性的新结果。我们还讨论了关于小数据解的存在性和正则性的一些结果。这些结果是基于Necas为研究一类偏微分方程解(时间整体)的存在性而发展的一种新方法，该方法给出了从二阶和一阶导数的L2范数的有界性出发的梯度逼近的几乎处处收敛。
In this paper we clarify and discuss some subtle features concerning the non-Newtonian fluid models which were considered by Malek, Necas and Růžicka.19 We establish new results regarding the stability of the rest state of mechanically isolated flows of such non-Newtonian fluids for arbitrary initial disturbances. We also discuss some results concerning the existence and regularity of solutions for small data. These results are based on a new method, giving convergence almost everywhere of approximations of gradients from boundedness of fraction of the L2-norm of the second and first derivatives, developed by Necas to study existence of solutions (global in time) to a class of partial differential equations.