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
SN - 0022-0396
VL - 266
SP - 3279
EP - 3309
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 6
ER -