Existence and uniqueness of the Hele-Shaw problem with injection
نویسنده
چکیده
This paper gives a new and short proof of existence and uniqueness of the Polubarinova-Galin equation. The existence proof is an application of the main theorem in Lin [2]. Furthermore, we can conclude that every strong solution can be approximated by many strong polynomial solutions locally in time.
منابع مشابه
Viscosity solutions of Hele-Shaw moving boundary problem for power-law fluid∗
Existence and uniqueness of solutions for Hele-shaw moving boundary problem for power-law fluid is established in the framework of viscosity solutions.
متن کاملTwo-phase Flow in Rotating Hele-shaw Cells with Coriolis Effects
The free boundary problem of a two phase flow in a rotating Hele-Shaw cell with Coriolis effects is studied. Existence and uniqueness of solutions near spheres is established, and the asymptotic stability and instability of the trivial solution is characterized in dependence on the fluid densities.
متن کاملOn 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 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.
متن کاملOn the gradient flow of a one-homogeneous functional
We consider the gradient flow of a one-homogeneous functional, whose dual involves the derivative of a constrained scalar function. We show in this case that the gradient flow is related to a weak, generalized formulation of a Hele-Shaw flow. The equivalence follows from a variational representation, which is a variant of well-known variational representations for the Hele-Shaw problem. As a co...
متن کامل