2019/01/11 by Craig Gin, Gin, Craig, Prabir Daripa +1 · 1 citation
Computer Science · Mathematics · #34L10 #34L15 #34L16 #76E17 #76S05 #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1901.03754
openalex publication_date 2019/01/11 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28
We perform a linear stability analysis of three-layer radial porous media and\nHele-Shaw flows with variable viscosity in the middle layer. A nonlinear change\nof variables results in an eigenvalue problem that has time-dependent\ncoefficients and eigenvalue-dependent boundary conditions. We study this\neigenvalue problem and find upper bounds on the spectrum. We also give a\ncharacterization of the eigenvalues and prescribe a measure for which the\neigenfunctions are complete in the corresponding L2 space. The limit as the\nviscous gradient goes to zero is compared with previous results on multi-layer\nradial flows. We then numerically compute the eigenvalues and obtain, among\nother results, optimal profiles within certain classes of functions.\n