Abstract:We study a model of electroconvection in which a two dimensional viscous fluid caries electrical charges and interacts with them. The system has global solutions, but in general the solutions do not have bounded mean. Tracking the mean, we associate to each solution a mean zero frame and show that in the mean zero frame the system has a compact, finite dimensional global attractor. If the fluid is forced only by electrical forces and no other body forces are present, then the attractor reduces to one point.

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中文翻译：

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电对流模型的长时间动力学

摘要：我们研究了一种二维粘性流体携带电荷并与之相互作用的电对流模型。系统有全局解，但一般来说解没有有界均值。跟踪均值，我们将每个解决方案与均值零帧相关联，并表明在均值零帧中系统具有紧凑的、有限维的全局吸引子。如果流体仅受到电力的推动，并且不存在其他体力，那么吸引子就会减少到一点。

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