Tresca摩擦条件下平面剪切流指数吸引子的存在性
On the existence of an exponential attractor for a planar shear flow with Tresca's friction condition
摘要：
我们考虑一个二维非定常Navier-Stokes剪切流与次微分边界条件的一部分边界的流域，即，与边界驱动受Tresca法律。存在一个唯一的全球时间解决所考虑的问题，这是由变分不等式。我们的目的是证明存在一个有限分数维的整体吸引子和一个指数吸引子的相关半群。我们使用的方法$l$ -轨迹。本研究的动机是从润滑理论的问题。
英文摘要：
We consider a two-dimensional nonstationary Navier-Stokes shear flow with a subdifferential boundary condition on a part of the boundary of the flow domain, namely, with a boundary driving subject to the Tresca law. There exists a unique global in time solution of the considered problem which is governed by a variational inequality. Our aim is to prove the existence of a global attractor of a finite fractional dimension and of an exponential attractor for the associated semigroup. We use the method of $l$-trajectories. This research is motivated by a problem from lubrication theory.
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