Non blowup of a generalized Boussinesq–Burgers system with nonlinear dispersion relation and large data.

Abstract We study the qualitative behavior of classical solutions to the Cauchy problem of a generalized Boussinesq–Burgers system in one space dimension. Assuming initial data belong to H 2 (R) and utilizing energy methods, we show that there exist unique global-in-time classical solutions to the Cauchy problem of the model, and the solutions converge to constant equilibrium states as time goes to infinity, regardless of the magnitude of the initial data. Moreover, it is shown that the viscous and inviscid models are consistent in the process of vanishing viscosity limit. Highlights • Model under consideration consists of a power-like dispersion relation. • Classical solutions exist globally for initial data with finite energy. • Constant equilibrium states are globally asymptotically stable. • Viscous system is consistent with inviscid system in vanishing viscosity limit. [ABSTRACT FROM AUTHOR]