In this paper, we consider the asymptotic behavior of an incompressible fluid around a bounded obstacle. By adapting the Schauder's estimate for stationary Navier–Stokes equation to improve the regularity, the problem is solved by using appropriate Carleman estimates. It should be noted that the minimal decaying rate for a general scalar equation is exp(−C|x|2+). However, the structure of the Navier–Stokes is special. Under the assumption for any nontrivial solution to be uniform bounded which is weaker than those in , we got the minimal decaying rate is exp(−C|x|[Formula presented]+) which is better than the results in general scalar cases.
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