Abstract

We study linear stability of a steady state for a generalization of the basic rheological Pokrovskii–Vinogradov model which describes the flows of melts and solutions of an incompressible viscoelastic polymeric medium in the nonisothermal case under the influence of a magnetic field. We prove that the corresponding linearized problem describing magnetohydrodynamic flows of polymers in an infinite plane channel has the following property: For some values of the conduction current which is given on the electrodes (i.e. at the channel boundaries), there exist solutions whose amplitude grows exponentially (in the class of functions periodic along the channel).

中文翻译：

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不可压缩聚合物流体的MHD模型：稳态的线性不稳定性

摘要

我们研究基本流变学Pokrovskii–Vinogradov模型的稳态的线性稳定性，该模型描述了在非等温情况下在磁场影响下的熔体流动和不可压缩粘弹性聚合物介质的溶液。我们证明，描述无限平面通道中聚合物的磁流体流动的相应线性化问题具有以下性质：对于在电极上（即，在通道边界处）给出的传导电流的某些值，存在振幅呈指数增长的解决方案（在沿通道周期性的功能类别中）。