Classical solutions for Hele-Shaw models with surface tension
نویسندگان
چکیده
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.
منابع مشابه
On Hele-shaw Models with Surface Tension
It is shown that surface tension effects on the free boundary have a regularizing effect for Hele-Shaw models, which implies existence and uniqueness of classical solutions for general initial domains.
متن کاملClassical solutions and stability results for Stokesian Hele-Shaw flows
In this paper we study a mathematical model for the motion of a Stokesian fluid in a Hele-Shaw cell surrounded by a gas at uniform pressure. The model is based on a non-Newtonian version of Darcy’s law for the bulk fluid, as suggested in [9, 12]. Besides a general existence and uniqueness result for classical solutions, it is also shown that classical solutions exist globally and tend to circle...
متن کاملTwo-dimensional Stokes and Hele-Shaw flows with free surfaces
We discuss the application of complex variable methods to Hele-Shaw flows and twodimensional Stokes flows, both with free boundaries. We outline the theory for the former, in the case where surface tension effects at the moving boundary are ignored. We review the application of complex variable methods to Stokes flows both with and without surface tension, and we explore the parallels between t...
متن کاملNon-trivial self-similar extinction solutions for a 3D Hele-Shaw suction problem
We show the existence of noncircular, self-similar solutions to the three-dimensional Hele-Shaw suction problem with surface tension regularisation up to complete extinction. In an appropriate scaling, these solutions are found as bifurcation solutions to a nonlocal elliptic equation of order three. The bifurcation parameter is the ratio of the suction speed and the surface tension coefficient....
متن کاملStability of self-similar extinction solutions for a 3D Hele-Shaw suction problem
We present a stability result for a class of non-trivial self-similarly vanishing solutions to a 3D Hele-Shaw moving boundary problem with surface tension and single-point suction. These solutions are domains that bifurcate from the trivial spherical solution. The moving domains have a geometric centre located at the suction point and they are axially symmetric. We show stability with respect t...
متن کامل