Backward behavior of solutions of the Kuramoto–Sivashinsky equation

We prove that any solution of the Kuramoto–Sivashinsky equation either belongs to the global attractor or it cannot be continued to a solution defined for all negative times. This extends a previous result of the first author who proved that solutions which do not belong to the global attractor have superexponential backward growth. A particular consequence of the result is that the global attractor can be characterized as the maximal invariant set.  2005 Elsevier Inc. All rights reserved