Details
| Original language | English |
|---|---|
| Pages (from-to) | 325-349 |
| Number of pages | 25 |
| Journal | Annali della Scuola Normale - Classe di Scienze |
| Volume | 9 |
| Issue number | 2 |
| Publication status | Published - 1 Dec 2010 |
Abstract
In this paper we study a mathematical model for the motion of a Stokesian fluid in a Hele-Shaw cell surrounded by a gas at uniform pressure. The model is based on a non-Newtonian version of Darcy's law for the bulk fluid, as suggested in [9, 12]. Besides a general existence and uniqueness result for classical solutions, it is also shown that classical solutions exist globally and tend to circles exponentially fast, provided the initial data is sufficiently close to a circle. Finally, our analysis discloses the influence of surface tension and the effective viscosity on the rate of convergence.
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Mathematics(all)
- Mathematics (miscellaneous)
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In: Annali della Scuola Normale - Classe di Scienze, Vol. 9, No. 2, 01.12.2010, p. 325-349.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Classical solutions and stability results for Stokesian Hele-Shaw flows
AU - Escher, Joachim
AU - Matioc, Anca Voichita
AU - Matioc, Bogdan-Vasile
PY - 2010/12/1
Y1 - 2010/12/1
N2 - In this paper we study a mathematical model for the motion of a Stokesian fluid in a Hele-Shaw cell surrounded by a gas at uniform pressure. The model is based on a non-Newtonian version of Darcy's law for the bulk fluid, as suggested in [9, 12]. Besides a general existence and uniqueness result for classical solutions, it is also shown that classical solutions exist globally and tend to circles exponentially fast, provided the initial data is sufficiently close to a circle. Finally, our analysis discloses the influence of surface tension and the effective viscosity on the rate of convergence.
AB - In this paper we study a mathematical model for the motion of a Stokesian fluid in a Hele-Shaw cell surrounded by a gas at uniform pressure. The model is based on a non-Newtonian version of Darcy's law for the bulk fluid, as suggested in [9, 12]. Besides a general existence and uniqueness result for classical solutions, it is also shown that classical solutions exist globally and tend to circles exponentially fast, provided the initial data is sufficiently close to a circle. Finally, our analysis discloses the influence of surface tension and the effective viscosity on the rate of convergence.
UR - http://www.scopus.com/inward/record.url?scp=78650434072&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:78650434072
VL - 9
SP - 325
EP - 349
JO - Annali della Scuola Normale - Classe di Scienze
JF - Annali della Scuola Normale - Classe di Scienze
SN - 0391-173X
IS - 2
ER -