An ill-posed problem in hydrodynamic stability of multi-layer Hele-Shaw flow
Fluid Dynamics
2020-08-31 v1 Mathematical Physics
math.MP
Abstract
An useful approximation for the displacement of two immiscible fluids in a porous medium is the Hele-Shaw model. We consider several liquids with different constant viscosities, inserted between the displacing fluids. The linear stability analysis of this model leads us to an ill-posed problem. The growth rates (in time) of the perturbations exist iff some compatibility conditions on the interfaces are verified. We prove that these conditions cannot be fulfilled.
Cite
@article{arxiv.2008.12561,
title = {An ill-posed problem in hydrodynamic stability of multi-layer Hele-Shaw flow},
author = {Gelu Paşa}},
journal= {arXiv preprint arXiv:2008.12561},
year = {2020}
}