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Asymptotically Almost Periodic and Almost Automorphic Solutions to the Non-autonomous Oseen-Navier-Stokes Equations
Ngoc Huy Nguyen
,
Thieu Huy Nguyen
,
Thi Ngoc Ha Vu
Abstract
In this paper, we investigate the existence, uniqueness and stability of asymptotically almost periodic and almost automorphic solutions to the non-autonomous Oseen-Navier-Stokes Equations (ONSE) in an unbounded domain $\varOmega \subset \mathbb {R}^{3}$ exterior to a rigid body $D$, i.e., $\varOmega =\mathbb {R}^{3}\backslash D$, with the data belonging to $L^p$-spaces and with the asymptotically almost periodic or almost automorphic external forces, respectively. Our method is based on the $L^p-L^q$ smoothness of the evolution family corresponding to linearized equations in combination with interpolation functors and fixed-point arguments.