Asymptotic behavior of solutions of the stationary Navier-Stokes equations in an exterior domain

Ching Lung Lin; Gunther Uhlmann; Jenn Nan Wang

doi:10.1512/iumj.2011.60.4490

Asymptotic behavior of solutions of the stationary Navier-Stokes equations in an exterior domain

Ching Lung Lin, Gunther Uhlmann, Jenn Nan Wang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

In this paper we are interested in the asymptotic behavior of an incompressible fluid around a bounded obstacle. The problem is described by the stationary Navier-Stokes equations in an exterior domain in ℝⁿ with n ≥ 2. We will show that under some assumptions, any nontrivial velocity field obeys a minimal decaying rate exp(-Ct² log t) at infinity. Our proof is based on appropriate Carleman estimates.

Original language	English
Pages (from-to)	2093-2106
Number of pages	14
Journal	Indiana University Mathematics Journal
Volume	60
Issue number	6
DOIs	https://doi.org/10.1512/iumj.2011.60.4490
Publication status	Published - 2011

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1512/iumj.2011.60.4490

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abstract = "In this paper we are interested in the asymptotic behavior of an incompressible fluid around a bounded obstacle. The problem is described by the stationary Navier-Stokes equations in an exterior domain in ℝn with n ≥ 2. We will show that under some assumptions, any nontrivial velocity field obeys a minimal decaying rate exp(-Ct2 log t) at infinity. Our proof is based on appropriate Carleman estimates.",

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AB - In this paper we are interested in the asymptotic behavior of an incompressible fluid around a bounded obstacle. The problem is described by the stationary Navier-Stokes equations in an exterior domain in ℝn with n ≥ 2. We will show that under some assumptions, any nontrivial velocity field obeys a minimal decaying rate exp(-Ct2 log t) at infinity. Our proof is based on appropriate Carleman estimates.

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Asymptotic behavior of solutions of the stationary Navier-Stokes equations in an exterior domain

Abstract

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