The stability of steady-state solutions of the equations governing two-dimensional,
homogeneous, incompressible fluid flow are analyzed in the context
of shear-flow in a channel. Both the linear and nonlinear theories are
reviewed and compared. In proving nonlinear stability of an equilibrium,
emphasis is placed on using the stability algorithm developed...
The main result of this paper is a proof of the existence of a solution
generated by a method for the variational assimilation of observational data
into the two-dimensional, incompressible Euler equations. The data are
assumed to be given by linear (measurement) functionals acting on the space
of functions representing...