Strong solutions for two-phase free boundary problems for a class of non-Newtonian fluids

Matthias Georg Hieber; Hirokazu Saito

doi:10.1007/s00028-016-0351-5

Strong solutions for two-phase free boundary problems for a class of non-Newtonian fluids

Matthias Georg Hieber, Hirokazu Saito

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 T_n 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	https://doi.org/10.1007/s00028-016-0351-5
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)

Access to Document

10.1007/s00028-016-0351-5

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AU - Saito, Hirokazu

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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.

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KW - strong solutions

KW - surface tension

KW - Two-phase free boundary problems

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