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DCDS-S

We study the uniform global attractor for a general nonautonomous
reaction-diffusion system without uniqueness using a new developed
framework of an evolutionary system. We prove the existence and the
structure of a weak uniform (with respect to a symbol space) global
attractor $\mathcal A$. Moreover, if the external force is normal,
we show that this attractor is in fact a strong uniform global
attractor. The existence of a uniform (with respect to the initial
time) global attractor $\mathcal A^0$ also holds in this case, but
its relation to $\mathcal A$ is not yet clear due to the
non-uniqueness feature of the system.

DCDS

The
existence and structure of uniform attractors in $V$ is proved for
nonautonomous 2D Navier-stokes equations on bounded domain with a
new class of external forces, termed

*normal*in $L_{l o c}^2(\mathbb R; H)$ (see Definition 3.1), which are translation bounded but not translation compact in $L_{l o c}^2(\mathbb R; H)$. To this end, some abstract results are established. First, a characterization on the existence of uniform attractor for a family of processes is presented by the concept of measure of noncompactness as well as a method to verify it. Then, the structure of the uniform attractor is obtained by constructing skew product flow on the extended phase space with weak topology. Finally, the uniform attractor of a process is identified with that of a family of processes with symbols in the closure of the translation family of the original symbol in a Banach space with weak topology.## Year of publication

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