Analyticity and nonexistence of classical steady Hele-Shaw fingers

✍ Scribed by Saleh Tanveer; Xuming Xie

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 447 KB
• Volume: 56
• Category: Article
• ISSN: 0010-3640
• DOI: 10.1002/cpa.3030

✦ Synopsis

Abstract

This paper concerns analyticity of a classical steadily translating finger in a Hele‐Shaw cell and nonexistence of solutions when relative finger width λ is smaller than ½. It is proved that any classical solution to the finger problem, if it exists for sufficiently small but nonzero surface tension and is close to some Saffman‐Taylor zero‐surface‐tension solution and satisfies some algebraic decay conditions at ∞, must belong to the analytic function space A~0~, as defined in Section 1, and chosen in a previous study [34] of existence of finger solutions. Further, it is proved that for any fixed λ ∈ (0, ½), there can be no classical steady finger solution when surface tension is sufficiently small, in disagreement with a previous conclusion based on numerical simulation. © 2002 Wiley Periodicals, Inc.