Global existence and decay rate of the Boussinesq–Burgers system with large initial data

Abstract

In this paper, we study the global existence and the long-time asymptotic behavior of classical solutions to the Cauchy problem for the Boussinesq–Burgers system with large initial data. More precisely, we first show that the classical solutions exist globally in time with large initial data by using the Lp (p>2) estimates other than the conventional L2 estimate. Then we prove that the global classical solutions converge to constant equilibrium states with an algebraic decay rate as time approaches infinity.