Abstract
Consider the two-phase free boundary problem subject to surface tension and gravitational forces for a class of non-Newtonian fluids with stress tensors Tn of the form (Formula presented.) for (Formula presented.), respectively, where the viscosity functions (Formula presented.) satisfy (Formula presented.) and (Formula presented.) for (Formula presented.). It is shown that for given (Formula presented.) this problem admits a unique strong solution on (0,T) provided the initial data are sufficiently small in their natural norms.
| Original language | English |
|---|---|
| Pages (from-to) | 1-24 |
| Number of pages | 24 |
| Journal | Journal of Evolution Equations |
| DOIs | |
| Publication status | Accepted/In press - 2016 Sep 19 |
| Externally published | Yes |
Keywords
- non-Newtonian fluids
- strong solutions
- surface tension
- Two-phase free boundary problems
ASJC Scopus subject areas
- Mathematics (miscellaneous)
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Hieber, M. G., & Saito, H. (Accepted/In press). Strong solutions for two-phase free boundary problems for a class of non-Newtonian fluids. Journal of Evolution Equations, 1-24. https://doi.org/10.1007/s00028-016-0351-5