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Volume 36, Issue 4
Existence and Nonlinear Stability of Stationary Solutions to the Viscous Two-Phase Flow Model in a Half Line

Hai-Liang Li & Shuang Zhao

DOI: 10.4208/cmr.2020-0063

Commun. Math. Res., 36 (2020), pp. 423-459.

Published online: 2020-11

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  • Abstract

The outflow problem for the viscous two-phase flow model in a half line is investigated in the present paper. The existence and uniqueness of the stationary solution is shown for both supersonic state and sonic state at spatial far field, and the nonlinear time stability of the stationary solution is also established in the weighted Sobolev space with either the exponential time decay rate for supersonic flow or the algebraic time decay rate for sonic flow.

  • Keywords

Two-phase flow, outflow problem, stationary solution, nonlinear stability.

  • AMS Subject Headings

35B35, 35B40, 76T10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-36-423, author = {Li , Hai-Liang and Zhao , Shuang}, title = {Existence and Nonlinear Stability of Stationary Solutions to the Viscous Two-Phase Flow Model in a Half Line}, journal = {Communications in Mathematical Research }, year = {2020}, volume = {36}, number = {4}, pages = {423--459}, abstract = {

The outflow problem for the viscous two-phase flow model in a half line is investigated in the present paper. The existence and uniqueness of the stationary solution is shown for both supersonic state and sonic state at spatial far field, and the nonlinear time stability of the stationary solution is also established in the weighted Sobolev space with either the exponential time decay rate for supersonic flow or the algebraic time decay rate for sonic flow.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2020-0063}, url = {http://global-sci.org/intro/article_detail/cmr/18361.html} }
TY - JOUR T1 - Existence and Nonlinear Stability of Stationary Solutions to the Viscous Two-Phase Flow Model in a Half Line AU - Li , Hai-Liang AU - Zhao , Shuang JO - Communications in Mathematical Research VL - 4 SP - 423 EP - 459 PY - 2020 DA - 2020/11 SN - 36 DO - http://doi.org/10.4208/cmr.2020-0063 UR - https://global-sci.org/intro/article_detail/cmr/18361.html KW - Two-phase flow, outflow problem, stationary solution, nonlinear stability. AB -

The outflow problem for the viscous two-phase flow model in a half line is investigated in the present paper. The existence and uniqueness of the stationary solution is shown for both supersonic state and sonic state at spatial far field, and the nonlinear time stability of the stationary solution is also established in the weighted Sobolev space with either the exponential time decay rate for supersonic flow or the algebraic time decay rate for sonic flow.

Li , Hai-Liang and Zhao , Shuang. (2020). Existence and Nonlinear Stability of Stationary Solutions to the Viscous Two-Phase Flow Model in a Half Line. Communications in Mathematical Research . 36 (4). 423-459. doi:10.4208/cmr.2020-0063
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