Review by Choice Review
Engineers evaluate the stability of simple dynamic systems by observing the response produced by departures from equilibrium. Fluid systems, however, are more difficult to analyze because most of the interesting applications involve irreversible, nonlinear motions. Analyzing the stability of flows forms the subject of this interesting research monograph, which extends a well-known technique developed by Lyapunov: if a positive input (the "Lyapunov functional") produces a response that eventually dies away, then the system is stable. Finding a Lyapunov functional that can yield clear cut results is often difficult; therefore, this book represents a significant contribution. Straughan shows how to use a generalized form of energy as a test input appropriate to a variety of applications in geophysics, chemical engineering, and electromagnetic rheology. Specific numerical results are quite impressive: Rayleigh numbers critical for the onset of Benard convection fall within a few percent of results obtained by conventional methods. One warning: readers will need a thorough familiarity with stability theory and variational methods, as well as an introductory background in functional analysis. These later topics were sketched somewhat hastily; better editing might have doubled the potential readership. Graduate level. M. B. Snyder; University of Nevada, Reno
Copyright American Library Association, used with permission.
Review by Choice Review
