Advances in Differential Equations

Classical solutions for Hele-Shaw models with surface tension

Joachim Escher and Gieri Simonett

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Abstract

It is shown that surface tension effects on the free boundary are regularizing for Hele-Shaw models. This implies, in particular, existence and uniqueness of classical solutions for a large class of initial data. As a consequence, we give a rigorous proof of the fact that homogeneous Hele-Shaw flows with positive surface tension are volume preserving and area shrinking.

Article information

Source
Adv. Differential Equations Volume 2, Number 4 (1997), 619-642.

Dates
First available in Project Euclid: 23 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366741151

Mathematical Reviews number (MathSciNet)
MR1441859

Zentralblatt MATH identifier
1023.35527

Subjects
Primary: 35Q99: None of the above, but in this section
Secondary: 35B40: Asymptotic behavior of solutions 35K55: Nonlinear parabolic equations 76D45: Capillarity (surface tension) [See also 76B45]

Citation

Escher, Joachim; Simonett, Gieri. Classical solutions for Hele-Shaw models with surface tension. Adv. Differential Equations 2 (1997), no. 4, 619--642. https://projecteuclid.org/euclid.ade/1366741151.


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