The global instability of uniform flows in non-one-dimensional regions

The conditions for the instability of flows or states, which are independent of time and coordinates, in extended non-one-dimensional regions are considered in a linear approximation. An extension of the idea of global instability, previously introduced for the one-dimensional case, is given. A method is proposed for weakly unstable flows, which enables one to investigate under what conditions perturbations, which grow without limit with time, and which do not depend on the specific form of boundary conditions (provided they are not degenerate), exist. The case of a two-dimensional rectangular region is considered in detail.