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

Pu Zhao Kow, Ching-Lung Lin

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)3279-3309
Number of pages31
JournalJournal of Differential Equations
Volume266
Issue number6
DOIs
Publication statusPublished - 2019 Mar 5

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Exterior Domain
Decay Rate
Navier-Stokes Equations
Schauder Estimates
Scalar
Carleman Estimate
Fluids
Nontrivial Solution
Navier-Stokes
Incompressible Fluid
Asymptotic Behavior
Regularity

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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On decay rate of solutions for the stationary Navier–Stokes equation in an exterior domain. / Kow, Pu Zhao; Lin, Ching-Lung.

In: Journal of Differential Equations, Vol. 266, No. 6, 05.03.2019, p. 3279-3309.

Research output: Contribution to journalArticle

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