Using trajectory attractor to construct trajectory statistical solution for the 3D incompressible micropolar flows

Abstract

Abstract In this article, we first prove the existence of trajectory attractor for the three‐dimensional incompressible micropolar fluids. This trajectory attractor is the minimal compact trajectory attracting set for the natural translation semigroup on the trajectory space. Then we construct the trajectory statistical solution for this micropolar fluids via the natural translation semigroup and trajectory attractor. In our construction the trajectory statistical solution is a space‐time probability measure, which is carried by the trajectory attractor and is invariant under the acting of the translation semigroup.

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