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arXiv · 1110.6248

Convergence Rates to Stationary Solutions of a Gas-liquid Model with External Forces and Vacuum

Long Fan·Qingqing Liu·Changjiang Zhu
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Abstract

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 assumptions on the initial date and $γ>1$, if $θ\in(0,\fracγ{2}]\cap(0,γ-1]\cap(0,1-αγ]$, 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 $θ\in(0,\fracγ{2}]\cap(0,γ-1)\cap(0,1-αγ]$, following the same idea in \cite{Fang-Zhang4}, we estimate the stabilization rate of the solution as time tends to infinity in the sense of $L^\infty$ norm.

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Long Fan, Qingqing Liu, Changjiang Zhu. 2011-10-28. Convergence Rates to Stationary Solutions of a Gas-liquid Model with External Forces and Vacuum. https://doi.org/10.1088/0951-7715%2F25%2F10%2F2875

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