Lp-theory for strong solutions to fluid-rigid body interaction in Newtonian and generalized Newtonian fluids
Lp-theory for strong solutions to fluid-rigid body interaction in Newtonian and generalized Newtonian fluids
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DOI：
10.1090/s0002-9947-2012-05652-2
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发表时间：
2012-08
影响因子：
1.3
通讯作者：
M. Geissert;K. Götze;Matthias Hieber
中科院分区：
文献类型：
--
作者：
M. Geissert;K. Götze;Matthias Hieber
考虑描述浸入牛顿或广义牛顿型粘性不可压缩流体中的刚体运动的方程组。所考虑的流体类别特别包括指数d ≥ 1的幂律型的剪切变稠或剪切变稠流体。我们开发了一种方法来证明，这个系统承认一个唯一的，本地的，在LP设置强的解决方案。在广义牛顿流体的情况下提出的方法是基于准线性发展方程的理论，并要求指数p满足条件p > 5。
Consider the system of equations describing the motion of a rigid body immersed in a viscous, incompressible fluid of Newtonian or generalized Newtonian type. The class of fluids considered includes in particular shearthinning or shear-thickening fluids of power-law type of exponent d ≥ 1. We develop a method to prove that this system admits a unique, local, strong solution in the Lp-setting. The approach presented in the case of generalized Newtonian fluids is based on the theory of quasi-linear evolution equations and requires that the exponent p satisfies the condition p > 5.