Abstract
In this paper, we investigate the initial value problem for the three dimensional generalized incompressible Oldroyd-B model. Based on the energy estimates and the tricky analytical skills, we prove that the problem always exists a unique global classical solution without any smallness restriction on the higher order spatial derivatives of initial data. Moreover, the optimal time-decay rates of solutions itself and the higher-order spatial derivatives of solutions are obtained without linear decay analysis. The result implies that the negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rate.
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