Abstract
In 1944, Landau ( Landau LD, Lifshitz EM (1987) Fluid mechanics. 2nd edition, Pergamon Press) formulated and solved the following three problems of hydrodynamic instability of the rupture surface in a perfect liquid.Problem of the tangential discontinuity. It is required to determine the stability of the interface between two liquid layers of different densities sliding relative to each other (Helmholtz solution, 1868). The Helmholtz solution is shown to be absolutely unstable.
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