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arXiv · 2212.00299

The viscous damping of three dimensional spherical gas bubble inside unbounded compressible liquid

Lifeng Zhao·Liangchen Zou
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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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Lifeng Zhao, Liangchen Zou. 2022-12-01. The viscous damping of three dimensional spherical gas bubble inside unbounded compressible liquid. https://arxiv.org/abs/2212.00299

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