Dynamical difference between nonlocal and local burgers equations

摘要

The Burgers equations is a prototypical simplied model for fluid dynamics. In this paper, the authors show that the maximal attractor of a nonlocal Burgers equation approaches the trival attractor of the usual local Burgers equation as the coefficient of the nonlocal integral term goes to zero. By a Cole-Hopf transformation, the nonlocal Burgers equation is transformed into a nonlocal heat equation and the authors then show that steady states of the nonlocal Burgers equation may change sign more than once, while all nontrivial steady states of the corresponding local Burgers equation only change sign once.