Advances in Differential Equations
- Adv. Differential Equations
- Volume 2, Number 4 (1997), 619-642.
Classical solutions for Hele-Shaw models with surface tension
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.
Adv. Differential Equations Volume 2, Number 4 (1997), 619-642.
First available in Project Euclid: 23 April 2013
Permanent link to this document
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. https://projecteuclid.org/euclid.ade/1366741151