Existence And Asymptotic Behavior Of Solution For The Boussinesq Equation With Damped Term Of Six Order

This paper discusses that the global existence of solution to the Cauchy problem of Boussinesq equations with damped term of sixth order. We give the physical meaning and the notations and research results of the equation in the introduction. The nonlinear generalized Bq equation with damped term of six order is and its linearized equation is Firstly the paper give the global existence and asymptotic behavior of solution to the Cauchy problem of (0.2) with the small initial value,then giving the global existence and asymptotic behavior of solution to the Cauchy problem of (0.1). Using Duhamel prin-ciple change (0.2) to its equivalence integral equation, then we get the global existence and decay property of solution to the equation of (0.2). Lastly we use the contraction mapping principle and integral estimates to give the existence and decays in the Besov space to the cauchy problem of the equation (0.1) in the case that the initial data are small.