Decay of global solutions of two nonlinear evolution equations

We study the decay of solutions of two nonlinear evolution equations: the Benjamin-Ono-Burgers and the Schrodinger-Burgers equations. We establish sharp rates ofL ² decay of global solutions to these problems, with initial dataU ₀(x)L ¹L ². The decay results of the solutions follow from thea priori L ² integral estimates and the Fourier transform. The standard argument relies on a technique that involves the splitting of the phase space into two time-dependent subdomains.