Well-posedness of a Hele-Shaw problem in general dimensions

2026/07/22 by Olga Turanova, Yuming Paul Zhang
Mathematics · #math.AP

paper · pdf

Abstract

We investigate a Hele-Shaw type free boundary problem in general spatial dimension. We establish a comparison principle and well-posedness for the problem using a notion of viscosity flows. An important feature of our work is that our hypotheses allow for the free boundary velocity to take negative values.

Related

• A Hele-Shaw problem with interior and free boundary oscillation: well-posedness and homogenization
• The Hele-Shaw semi-flow
• From the free boundary condition for Hele-Shaw to a fractional parabolic equation
• An efficient numerical method for estimating the average free boundary velocity in an inhomogeneous Hele-Shaw problem
• On a Generalized Two-Fluid Hele-Shaw Flow