### Abstract

We study the inviscid limit problem of incompressible flows in the presence of both impermeable regular boundaries and a hypersurface transversal to the boundary across which the inviscid flow has a discontinuity jump. In the former case, boundary layers have been introduced by Prandtl as correctors near the boundary between the inviscid and viscous flows. In the latter case, the viscosity smoothes out the discontinuity jump by creating a transition layer which has the same amplitude and thickness as the Prandtl layer. In the neighbourhood of the intersection of the impermeable boundary and of the hypersurface, interactions between the boundary and the transition layers must then be considered. In this paper, we initiate a mathematical study of this interaction and carry out a strong convergence in the inviscid limit for the case of the plane-parallel flows introduced by Di Perna and Majda (1987 Commun. Math. Phys. 108 667-89).

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

Pages (from-to) | 3327-3342 |

Number of pages | 16 |

Journal | Nonlinearity |

Volume | 25 |

Issue number | 12 |

DOIs | |

State | Published - Dec 1 2012 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics

### Cite this

*Nonlinearity*,

*25*(12), 3327-3342. https://doi.org/10.1088/0951-7715/25/12/3327

}

*Nonlinearity*, vol. 25, no. 12, pp. 3327-3342. https://doi.org/10.1088/0951-7715/25/12/3327

**Boundary-layer interactions in the plane-parallel incompressible flows.** / Nguyen, Toan T.; Sueur, Franck.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Boundary-layer interactions in the plane-parallel incompressible flows

AU - Nguyen, Toan T.

AU - Sueur, Franck

PY - 2012/12/1

Y1 - 2012/12/1

N2 - We study the inviscid limit problem of incompressible flows in the presence of both impermeable regular boundaries and a hypersurface transversal to the boundary across which the inviscid flow has a discontinuity jump. In the former case, boundary layers have been introduced by Prandtl as correctors near the boundary between the inviscid and viscous flows. In the latter case, the viscosity smoothes out the discontinuity jump by creating a transition layer which has the same amplitude and thickness as the Prandtl layer. In the neighbourhood of the intersection of the impermeable boundary and of the hypersurface, interactions between the boundary and the transition layers must then be considered. In this paper, we initiate a mathematical study of this interaction and carry out a strong convergence in the inviscid limit for the case of the plane-parallel flows introduced by Di Perna and Majda (1987 Commun. Math. Phys. 108 667-89).

AB - We study the inviscid limit problem of incompressible flows in the presence of both impermeable regular boundaries and a hypersurface transversal to the boundary across which the inviscid flow has a discontinuity jump. In the former case, boundary layers have been introduced by Prandtl as correctors near the boundary between the inviscid and viscous flows. In the latter case, the viscosity smoothes out the discontinuity jump by creating a transition layer which has the same amplitude and thickness as the Prandtl layer. In the neighbourhood of the intersection of the impermeable boundary and of the hypersurface, interactions between the boundary and the transition layers must then be considered. In this paper, we initiate a mathematical study of this interaction and carry out a strong convergence in the inviscid limit for the case of the plane-parallel flows introduced by Di Perna and Majda (1987 Commun. Math. Phys. 108 667-89).

UR - http://www.scopus.com/inward/record.url?scp=84869122179&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869122179&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/25/12/3327

DO - 10.1088/0951-7715/25/12/3327

M3 - Article

AN - SCOPUS:84869122179

VL - 25

SP - 3327

EP - 3342

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 12

ER -