Nonexistence For The "Missing"Similarity Boundary-Layer Flow
Joseph E. Paullet · 2014
This note considers the boundary value problem φ(η) + λφ(η) + φ(η) = 0, η ≥ 0, λ > 0, subject to φ(0) = 1 and φ(∞) = 0, 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.