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
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U2 - 10.1007/s00028-016-0351-5
DO - 10.1007/s00028-016-0351-5
M3 - Article
AN - SCOPUS:84988402612
SP - 1
EP - 24
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
SN - 1424-3199
ER -