Asymptotic stability of the compressible gas-liquid model with well-formation interaction and gravity

作者：Evje, Steinar; Liu, Qingqing; Zhu, Changjiang^*

来源：Journal of Differential Equations, 2014, 257(9): 3226-3271.

DOI：10.1016/j.jde.2014.06.012

• Two-phase flow
• Stationary solutions
• Convergence rates

In this paper we are concerned with the initial-boundary value problem of the compressible gas-liquid model with well-formation interaction and gravity. The asymptotic behavior of solutions to steady states is established. Also the time-decay rates of perturbed solutions in the sense of L-infinity norm are obtained under some suitable assumptions on the initial date, if gamma > 1 (associated with pressure law of gas) and beta is an element of (0, gamma/2) boolean AND (0, gamma - alpha gamma) boolean AND (0, gamma alpha gamma/3] where beta characterizes the viscosity coefficient and alpha describes the mass decay rate at the boundary. A main purpose of this work is to clarify the role played by the well-reservoir interaction term. The analysis demonstrates that it is essential to take into account information about sign as well as size of the interaction term in order to obtain time-independent estimates when it operates in combination with gravity.

• 出版日期2014-11-1
• 单位华中师范大学