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 |
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Keywords
- non-Newtonian fluids
- strong solutions
- surface tension
- Two-phase free boundary problems
ASJC Scopus subject areas
- Mathematics (miscellaneous)
Cite this
Strong solutions for two-phase free boundary problems for a class of non-Newtonian fluids. / Hieber, Matthias Georg; Saito, Hirokazu.
In: Journal of Evolution Equations, 19.09.2016, p. 1-24.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Strong solutions for two-phase free boundary problems for a class of non-Newtonian fluids
AU - Hieber, Matthias Georg
AU - Saito, Hirokazu
PY - 2016/9/19
Y1 - 2016/9/19
N2 - 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.
AB - 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.
KW - non-Newtonian fluids
KW - strong solutions
KW - surface tension
KW - Two-phase free boundary problems
UR - http://www.scopus.com/inward/record.url?scp=84988402612&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84988402612&partnerID=8YFLogxK
U2 - 10.1007/s00028-016-0351-5
DO - 10.1007/s00028-016-0351-5
M3 - Article
SP - 1
EP - 24
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
SN - 1424-3199
ER -