The boundedness and upper semicontinuity of the pullback attractors for a 2D micropolar fluid flows with delay

Abstract

<p style='text-indent:20px;'>In this paper, two properties of the pullback attractor for a 2D non-autonomous micropolar fluid flows with delay on unbounded domains are investigated. First, we establish the <inline-formula><tex-math id="M1">$ H^1 $</tex-math></inline-formula>-boundedness of the pullback attractor. Further, with an additional regularity limit on the force and moment with respect to time t, we remark the <inline-formula><tex-math id="M2">$ H^2 $</tex-math></inline-formula>-boundedness of the pullback attractor. Then, we verify the upper semicontinuity of the pullback attractor with respect to the domains.</p>