TY - JOUR

T1 - On decay rate of solutions for the stationary Navier–Stokes equation in an exterior domain

AU - Kow, Pu Zhao

AU - Lin, Ching Lung

N1 - Publisher Copyright:
© 2018 Elsevier Inc.

PY - 2019/3/5

Y1 - 2019/3/5

N2 - 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 [10], we got the minimal decaying rate is exp(−C|x|[Formula presented]+) which is better than the results in general scalar cases.

AB - 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 [10], 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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U2 - 10.1016/j.jde.2018.09.002

DO - 10.1016/j.jde.2018.09.002

M3 - Article

AN - SCOPUS:85052917427

VL - 266

SP - 3279

EP - 3309

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 6

ER -