Mathematics > Analysis of PDEs
[Submitted on 1 Dec 2022
]
Title: The viscous damping of three dimensional spherical gas bubble inside unbounded compressible liquid
Title: 三维球形气体气泡在无限可压缩液体中的粘性阻尼
Abstract: The present paper considers a homogeneous bubble inside an unbounded polytropic compressible liquid with viscosity. The system is governed by the Navier-Stokes equation with free boundary which is determined by the kinematic and dynamic boundary conditions on the bubble-liquid interface. The global existence of solution is proved, and the $\dot{H}^1$ asymptotic stability of the spherical equilibrium in terms of viscous damping together with a explicit decay rate is given in bare energy methods.
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