THE DOUBLE LAPLACIAN GROWTH

The dynamics of the idealized Laplacian growth (or the Hele-Shaw problem) can be approximated by the Poiselle flow which in appropriate units takes the form of the Darcy law. In this paper we account for the liquid inertia in the Hele-Shaw problem at zero surface tension limit. The Laplace dynamics for the pressure is extended here with one more for the velocity potential for which we call this growth process the Double Laplacian. The application of the conformal mappings technique leads to doubled dynamics for both the conformal map and the complex potential, which is presented in the paper for the radial and the planar growth. We apply the stability analysis and discuss the integrability for the stated problem