Convergence Rates To Stationary Solutions Of A Gas-liquid Model With External Forces And Vacuum

In this paper, we study the asymptotic behavior of solutions to a Gas-liquid model with external forces and general pressure law. Under some suitable assump-tions on the initial date, if γ>1and θ∈(0,γ/2]∩(0,γ-1]∩(0,1-αγ], we prove the weak solution (cQ(x,t),u(x,t)) behavior asymptotically to the stationary one by adapting and modifying the technique of weighted estimates. In addition, if θ(0,γ/2]∩(0,γ-1)∩(0,1-αγ], following the same idea in [8], we estimate the stabilization rate of the solution as time tends to infinity in the sense of L∞norm.