Advances in Differential Equations

Classical solutions for Hele-Shaw models with surface tension

Joachim Escher and Gieri Simonett

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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

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

First available in Project Euclid: 23 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]


Escher, Joachim; Simonett, Gieri. Classical solutions for Hele-Shaw models with surface tension. Adv. Differential Equations 2 (1997), no. 4, 619--642.

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