Classical solvability of the radial viscous fingering problem in a Hele-Shaw cell

  • Tani Atusi, tani@math.keio.ac.jp Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan
  • Tani Hisasi, htani0926@tamu.edu Department of Mechanical Engineering, Texas A&M University, TX 77843-3123, USA
Keywords: radial viscous fingering, Hele-Shaw problem, unique classical solution

Abstract

We discuss a single-phase radial viscous fingering problem in a Hele–Shaw cell, which is a nonlinear problem with a free boundary for an elliptic equation. Unlike the Stefan problem for heat equation Hele–Shaw problem is of hydrodynamic type. In this paper a single-phase Hele–Shaw problem in a radial flow geometry admits a unique classical solution by applying the same method as for Stefan problem and justifying the vanishing the coefficient of the derivative with respect to time in a parabolic equation.

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How to Cite
Tani, A. and Tani, H. ( ) “Classical solvability of the radial viscous fingering problem in a Hele-Shaw cell”, Mathematical notes of NEFU, 25(3), pp. 92-114. doi: https://doi.org/10.25587/SVFU.2018.99.16953.
Section
Mathematics