### Abstract

which arises in certain situations of boundary layer flow. Previous work on the problem established the existence of a λ_{min} ∈ [1; 2/√3] such that solutions exist for λ ≥ λ_{min}. It has been conjectured that for λ < λ_{min} no solution exists. We partially resolve this conjecture by proving that for λ ≤√2/3 ≈:8165 no solution to the boundary value problem exists.

This note considers the boundary value problem.

ϕʺ(η) + λϕʹ(η) + ϕ(η)^{2} = 0, η ≥ 0, λ > 0,.

subject to.

ϕ(0) = 1 and ϕ(∞) = 0,.

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

Pages (from-to) | 123-126 |

Number of pages | 4 |

Journal | Applied Mathematics E - Notes |

Volume | 14 |

State | Published - Jan 1 2014 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics

### Cite this

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*Applied Mathematics E - Notes*, vol. 14, pp. 123-126.

**Nonexistence for the "missing" similarity boundary-layer flow.** / Paullet, Joseph E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Nonexistence for the "missing" similarity boundary-layer flow

AU - Paullet, Joseph E.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - which arises in certain situations of boundary layer flow. Previous work on the problem established the existence of a λmin ∈ [1; 2/√3] such that solutions exist for λ ≥ λmin. It has been conjectured that for λ < λmin no solution exists. We partially resolve this conjecture by proving that for λ ≤√2/3 ≈:8165 no solution to the boundary value problem exists.This note considers the boundary value problem.ϕʺ(η) + λϕʹ(η) + ϕ(η)2 = 0, η ≥ 0, λ > 0,.subject to.ϕ(0) = 1 and ϕ(∞) = 0,.

AB - which arises in certain situations of boundary layer flow. Previous work on the problem established the existence of a λmin ∈ [1; 2/√3] such that solutions exist for λ ≥ λmin. It has been conjectured that for λ < λmin no solution exists. We partially resolve this conjecture by proving that for λ ≤√2/3 ≈:8165 no solution to the boundary value problem exists.This note considers the boundary value problem.ϕʺ(η) + λϕʹ(η) + ϕ(η)2 = 0, η ≥ 0, λ > 0,.subject to.ϕ(0) = 1 and ϕ(∞) = 0,.

UR - http://www.scopus.com/inward/record.url?scp=84908273133&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84908273133&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84908273133

VL - 14

SP - 123

EP - 126

JO - Applied Mathematics E - Notes

JF - Applied Mathematics E - Notes

SN - 1607-2510

ER -