Regular attractor for damped KdV‐Burgers equations on R

Abstract

We study the well‐posedness and dynamic behavior for the KdV‐Burgers equation with a force on R. We establish Lp−Lq estimates of the evolution , as an application we obtain the local well‐posedness. Then the global well‐posedness follows from a uniform estimate for solutions as tgoes to infinity. Next, we prove the asymptotical regularity of solutions in space and by the smoothing effect of . The regularity and the asymptotical compactness in L2 yields the asymptotical compactness in by an interpolation arguement. Finally, we conclude the existence of an globalattractor.