Tuned Mullins-Sekerka instability: exact results.

Mullins-Sekerka's instability at 3D self-similar growth of a spherical seed crystal in an undercooled fluid is discussed. The exact solution of the linearized stability problem is obtained. It is quite different from the conventional results of the quasisteady approximation. The instability occurs much weaker, so that instead of exponential growth in time, unstable modes exhibit just power-law-growth. The relative growth rates of different modes vary in time and depend on their initial amplitudes. It allows control over the growth of each mode individually and tailoring the instability, to obtain a desired shape of the growing crystal at a given time.