Abstract
The purpose of this work is to study a one phase Hele-Shaw fluid flow occupying a time variable domain \(\Omega (t)\), due to the injection of the fluid with a constant rate at a single point of the initial domain \(\Omega (0)\), and in the presence of a fixed solid body \(\Omega _0\). We show the short time existence and uniqueness of the solution for the corresponding boundary value problem in the three dimensional case and in the absence of surface tension.
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