LOCAL WELL-POSEDNESS FOR A 3D LIQUID-GAS TWO PHASE MODEL WITH VACUUM

Xiuhui Yang

doi:10.11948/20210503

2022 Volume 12 Issue 6

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Xiuhui Yang. LOCAL WELL-POSEDNESS FOR A 3D LIQUID-GAS TWO PHASE MODEL WITH VACUUM[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2386-2395. doi: 10.11948/20210503

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Xiuhui Yang. LOCAL WELL-POSEDNESS FOR A 3D LIQUID-GAS TWO PHASE MODEL WITH VACUUM[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2386-2395. doi: 10.11948/20210503

LOCAL WELL-POSEDNESS FOR A 3D LIQUID-GAS TWO PHASE MODEL WITH VACUUM

Xiuhui Yang^†,

†.
Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 2100016, China

Author Bio: Xiuhui Yang, Email address: xhyang@nuaa.edu.cn

Abstract

Abstract

In this paper we prove the local well-posedness of strong solutions to a 3D liquid-gas two-phase flow model with vacuum in a bounded domain without the standard compatibility conditions.
- Liquid-gas two-phase flow model /
- vacuum /
- local well-posedness
MSC: 76T10, 35Q35, 35D35, 76N10

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References

[1]	S. Chen and C. Zhu, Existence of weak solutions to the steady two-phase flow, Commun. Math. Sci., 2019, 17, 1699–1712. Google Scholar
[2]	H. J. Choe and H. Kim, Strong solutions of the Navier-Stokes equations for isentropic compressible fluids, J. Differential Equations, 2003, 190, 504–523. Google Scholar
[3]	S. Evje and K. H. Karlsen, Global existence of weak solutions for a viscous two-phase model, J. Differential Equations, 2008, 245, 2660–2703. doi: 10.1016/j.jde.2007.10.032 CrossRef Google Scholar
[4]	S. Evje and H. Wen, Weak solutions of a two-phase Navier-Stokes model with a general slip law, J. Funct. Anal., 2015, 268, 93–139. doi: 10.1016/j.jfa.2014.10.019 CrossRef Google Scholar
[5]	H. Gong, J. Li, X. Liu and X. Zhang, Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum, Commun. Math. Sci., 2020, 18, 1891–1909. doi: 10.4310/CMS.2020.v18.n7.a4 CrossRef Google Scholar
[6]	Z. Guo, J. Yang and L. Yao, Global strong solution for a three-dimensional viscous liquid-gas two-phase flow model with vacuum, J. Math. Phys., 2011, 52, 14, Paper No. 093102. Google Scholar
[7]	X. Huang, On local strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with vacuum, Sci. China Math., 2021, 64, 1771–1788. Google Scholar
[8]	Y. Li, Y. Sun and E. Zatorska, Large time behavior for a compressible two-fluid model with algebraic pressure closure and large initial data, Nonlinearity, 2020, 33, 4075–4094. doi: 10.1088/1361-6544/ab801c CrossRef Google Scholar
[9]	G. Metivier and S. Schochet, The incompressible limit of the non-isentropic Euler equations, Arch. Ration. Mech. Anal., 2001, 158, 61–90. doi: 10.1007/PL00004241 CrossRef Google Scholar
[10]	H. Wen, L. Yao and C. Zhu, A blow-up criterion of strong solution to a 3D viscous liquid-gas two-phase flow model with vacuum, J. Math. Pures Appl., 2012, 97, 204–229. Google Scholar
[11]	H. Wen, L. Yao and C. Zhu, Review on mathematical analysis of some two-phase flow models, Acta. Math. Sci. Ser. B(Engl. Ed. ), 2018, 38, 1617–1636. Google Scholar
[12]	G. Wu and Y. Zhang, Global analysis of strong solutions for the viscous liquid-gas two-phase flow model in a bounded domain, Discrete Contin. Dyn. Syst. Ser. B, 2018, 23, 1411–1429. Google Scholar
[13]	L. Yao, J. Yang and Z. Guo, Global classical solution for a three-dimensional viscous liquid-gas two-fluid flow model with vacuum, Acta. Math. Appl. Sin. Engl. Ser., 2014, 30, 989–1006. Google Scholar
[14]	X. Yang, Local well-posedness of the compressible Navier-Stokes-Smoluchowski equations with vacuum, J. Math. Anal. Appl., 2020, 485, 8, Paper No. 123792. Google Scholar
[15]	Y. Zhang, Weak solutions for an inviscid two-phase flow model in physical vacuum, J. Differential Equations, 2018, 265, 6251–6294. Google Scholar