An ill-posed problem in hydrodynamic stability of multi-layer Hele-Shaw flow
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2020
- DOI:
- 10.48550/arXiv.2008.12561
- arXiv:
- arXiv:2008.12561
- Bibcode:
- 2020arXiv200812561P
- Keywords:
-
- Physics - Fluid Dynamics;
- Mathematical Physics;
- 34B09;
- 34D20;
- 35C09;
- 35J20;
- 76S05