ON THE ARNOLD STABILITY OF A SOLID IN A PLANE STEADY FLOW OF AN IDEALINCOMPRESSIBLE FLUID

We study the stability of a rigid body in a steady rotational flow of an inviscid incompressible fluid. We consider the two-dimensional prob lem: a body is an infinite cylinder with arbitrary cross section movin g perpendicularly to its axis, a flow is two-dimensional, i.e., it doe s not depend on the coordinate along the axis of a cylinder; both body and fluid are in a two-dimensional bounded domain with an arbitrary s mooth boundary. Arnold's method is exploited to obtain sufficient cond itions for linear stability of an equilibrium of a body in a steady ro tational flow. We first establish a new energy-type variational princi ple which is a natural generalization of the well-known Amold's result (1965a, 1966) to the system ''body + fluid.'' Then, by Arnold's techn ique, a general sufficient condition for linear stability is obtained.