On the nonlinear instability of the solutions of hydrodynamic-type systems

Abstract

New exact solutions (including periodic) of three-dimensional nonstationary Navier-Stokes equations containing arbitrary functions are described. The problems of the nonlinear stability/instability of the solutions have been analyzed. It has been found that a feature of a wide class of the solutions of hydrodynamic-type systems is their instability. It has been shown that instability can occur not only at sufficiently large Reynolds numbers, but also at arbitrary small Reynolds numbers (and can be independent of the fluid velocity profile). A general physical interpretation of the solution under consideration is given. It is important to note that the instability of the solutions has been proven using a new exact method (without any assumptions and approximations), which can be useful for analyzing other nonlinear physical models and phenomena.