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Decay of the 3D inviscid liquid–gas two-phase flow model

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Abstract

We establish the optimal \({L^{p}-L^{2}(1 \leq p < 6/5)}\) time decay rates of the solution to the Cauchy problem for the 3D inviscid liquid–gas two-phase flow model and analyze the influences of the damping on the qualitative behaviors of solution. Compared with the viscous liquid–gas two-phase flow model (Zhang and Zhu in J Differ Equ 258:2315–2338, 2015), our results imply that the friction effect of the damping is stronger than the dissipation effect of the viscosities and enhances the decay rate of the velocity. Our proof is based on Hodge decomposition technique, the \({L^{p}-L^{2}}\) estimates for the linearized equations and an elaborate energy method.

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  1. Department of Mathematics, Hunan Institute of Science and Technology, Yueyang, 414006, China

    Yinghui Zhang

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Zhang, Y. Decay of the 3D inviscid liquid–gas two-phase flow model. Z. Angew. Math. Phys. 67, 54 (2016). https://doi.org/10.1007/s00033-016-0658-7

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  • DOI: https://doi.org/10.1007/s00033-016-0658-7

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