ATTRACTORS FOR NONCOMPACT SEMIGROUPS VIA ENERGY EQUATIONS

The energy-equation approach used to prove the existence of the global attractor by establishing the so-called asymptotic compactness proper ty of the semigroup is considered, and a general formulation that can handle a number of weakly damped hyperbolic equations and parabolic eq uations on either bounded or unbounded spatial domains is presented. A s examples, three specific and physically relevant problems are consid ered, namely the flows of a second-grade fluid, the flows of a Newtoni an fluid in an infinite channel past an obstacle, and a weakly damped, forced Korteweg-de Vries equation on the whole line.