### Abstract

In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity.

Original language | English (US) |
---|---|

Pages (from-to) | 335-354 |

Number of pages | 20 |

Journal | Communications in Partial Differential Equations |

Volume | 26 |

Issue number | 1-2 |

State | Published - 2001 |

### Fingerprint

### Keywords

- Asymptotic analysis
- Boundary layer
- Explicit solutions
- Navier-Stokes equations
- Stokes equations
- Zero viscosity

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Communications in Partial Differential Equations*,

*26*(1-2), 335-354.

**Asymptotic analysis of the linearized Navier-Stokes equation on an exterior circular domain : Explicit solution and the zero viscosity limit.** / Lombardo, Maria Carmela; Caflisch, Russel; Sammartino, Marco.

Research output: Contribution to journal › Article

*Communications in Partial Differential Equations*, vol. 26, no. 1-2, pp. 335-354.

}

TY - JOUR

T1 - Asymptotic analysis of the linearized Navier-Stokes equation on an exterior circular domain

T2 - Explicit solution and the zero viscosity limit

AU - Lombardo, Maria Carmela

AU - Caflisch, Russel

AU - Sammartino, Marco

PY - 2001

Y1 - 2001

N2 - In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity.

AB - In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity.

KW - Asymptotic analysis

KW - Boundary layer

KW - Explicit solutions

KW - Navier-Stokes equations

KW - Stokes equations

KW - Zero viscosity

UR - http://www.scopus.com/inward/record.url?scp=3142749306&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3142749306&partnerID=8YFLogxK

M3 - Article

VL - 26

SP - 335

EP - 354

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 1-2

ER -