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A new blowup criterion for strong solutions to a viscous liquid-gas two-phase flow model with vacuum in three dimensions
1. | Department of Mathematics, South China University of Technology, Guangzhou 510641, China, China |
References:
[1] |
P. Acquistapace, On BMO regularity for linear elliptic systems, Ann. Mat. Pura Appl., 161 (1992), 231-269.
doi: 10.1007/BF01759640. |
[2] |
H. B. Cui, H. Y. Wen and H. Y. Yin, Global classical solutions of viscous liquid-gas two-phase flow model, Math. Meth. Appl. Sci., 36 (2013), 567-583.
doi: 10.1002/mma.2614. |
[3] |
S. Evje, T. Flåtten and H. A. Friis, Global weak solutions for a viscous liquid-gas model with transition to single-phase gas flow and vacuum, Nonlinear Anal., TMA, 70 (2009), 3864-3886.
doi: 10.1016/j.na.2008.07.043. |
[4] |
S. Evje and K. H. Karlsen, Global existence of weak solutions for a viscous two-phase model, J. Differential Equations, 245 (2008), 2660-2703.
doi: 10.1016/j.jde.2007.10.032. |
[5] |
S. Evje and K. H. Karlsen, Global weak solutions for a viscous liquid-gas model with singular pressure law, Commun. Pure Appl. Anal., 8 (2009), 1867-1894.
doi: 10.3934/cpaa.2009.8.1867. |
[6] |
Z. H. Guo, J. Yang and L. Yao, Global strong solution for a three-dimensional viscous liquid-gas two-phase flowmodelwith vacuum, Journal of Mathematical Physics, 52 (2011), 093102, 14pp. |
[7] |
C. C. Hao and H. L. Li, Well-posedness for a multidimensional viscous liquid-gas two-phase flow model, SIAM J. Math. Anal., 44 (2012), 1304-1332.
doi: 10.1137/110851602. |
[8] |
M. Ishii, Thermo-Fluid Dynamic Theory of Two-Phase Flow, Eyrolles, Paris, 1975. |
[9] |
O. A. Ladyzenskaja, V. A. Solonikov and N. N. Ural'ceva, Linear and Quasilinear Equation of Parabolic Type, Amer. Math. Soc., Providence RI, 1968. |
[10] |
A. Prosperetti and G. Tryggvason (Editors), Computational Methods for Multiphase Flow, Cambridge University Press, Cambridge, 2009. |
[11] |
Y. Z. Sun, C. Wang and Z. F. Zhang, A Beale-Kato-Majda blow-up criterion for the 3-D compressible Navier-Stokes equations, J. Math. Pures Appl., 95 (2011), 36-47.
doi: 10.1016/j.matpur.2010.08.001. |
[12] |
V. A. Vaigant and A. V. Kazhikhov, On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscosity fluid, Siberian Math. J., 36 (1995), 1108-1141.
doi: 10.1007/BF02106835. |
[13] |
H. Y. Wen, L. Yao and C. J. Zhu, A blow-up criterion of strong solution to a 3D viscous liquid-gas two-phase flow model with vacuum, J.Math.Pures Appl., 97 (2012), 204-229.
doi: 10.1016/j.matpur.2011.09.005. |
[14] |
H. Y. Wen and C. J. Zhu, Blow-up criterions of strong solutions to 3D compressible Navier-Stokes equations with vacuum, Advances in Mathematics, 248 (2013), 534-572.
doi: 10.1016/j.aim.2013.07.018. |
[15] |
L. Yao and C. J. Zhu, Free boundary value problem for a viscous two-phase model with mass-dependent viscosity, J. Differential Equations, 247 (2009), 2705-2739.
doi: 10.1016/j.jde.2009.07.013. |
[16] |
L. Yao and C. J. Zhu, Existence and uniqueness of global weak solution to a two-phase flow model with vacuum, Math. Ann., 349 (2011), 903-928.
doi: 10.1007/s00208-010-0544-0. |
[17] |
L. Yao, T. Zhang and C. J. Zhu, Existence and asymptotic behavior of global weak solutions to a 2D viscous liquid-gas two-phase flow model, SIAM J. Math. Anal., 42 (2010), 1874-1897.
doi: 10.1137/100785302. |
[18] |
L. Yao, T. Zhang and C. J. Zhu, A blow-up criterion for a 2D viscous liquid-gas two-phase flow model, J. Differential Equations, 250 (2011), 3362-3378.
doi: 10.1016/j.jde.2010.12.006. |
show all references
References:
[1] |
P. Acquistapace, On BMO regularity for linear elliptic systems, Ann. Mat. Pura Appl., 161 (1992), 231-269.
doi: 10.1007/BF01759640. |
[2] |
H. B. Cui, H. Y. Wen and H. Y. Yin, Global classical solutions of viscous liquid-gas two-phase flow model, Math. Meth. Appl. Sci., 36 (2013), 567-583.
doi: 10.1002/mma.2614. |
[3] |
S. Evje, T. Flåtten and H. A. Friis, Global weak solutions for a viscous liquid-gas model with transition to single-phase gas flow and vacuum, Nonlinear Anal., TMA, 70 (2009), 3864-3886.
doi: 10.1016/j.na.2008.07.043. |
[4] |
S. Evje and K. H. Karlsen, Global existence of weak solutions for a viscous two-phase model, J. Differential Equations, 245 (2008), 2660-2703.
doi: 10.1016/j.jde.2007.10.032. |
[5] |
S. Evje and K. H. Karlsen, Global weak solutions for a viscous liquid-gas model with singular pressure law, Commun. Pure Appl. Anal., 8 (2009), 1867-1894.
doi: 10.3934/cpaa.2009.8.1867. |
[6] |
Z. H. Guo, J. Yang and L. Yao, Global strong solution for a three-dimensional viscous liquid-gas two-phase flowmodelwith vacuum, Journal of Mathematical Physics, 52 (2011), 093102, 14pp. |
[7] |
C. C. Hao and H. L. Li, Well-posedness for a multidimensional viscous liquid-gas two-phase flow model, SIAM J. Math. Anal., 44 (2012), 1304-1332.
doi: 10.1137/110851602. |
[8] |
M. Ishii, Thermo-Fluid Dynamic Theory of Two-Phase Flow, Eyrolles, Paris, 1975. |
[9] |
O. A. Ladyzenskaja, V. A. Solonikov and N. N. Ural'ceva, Linear and Quasilinear Equation of Parabolic Type, Amer. Math. Soc., Providence RI, 1968. |
[10] |
A. Prosperetti and G. Tryggvason (Editors), Computational Methods for Multiphase Flow, Cambridge University Press, Cambridge, 2009. |
[11] |
Y. Z. Sun, C. Wang and Z. F. Zhang, A Beale-Kato-Majda blow-up criterion for the 3-D compressible Navier-Stokes equations, J. Math. Pures Appl., 95 (2011), 36-47.
doi: 10.1016/j.matpur.2010.08.001. |
[12] |
V. A. Vaigant and A. V. Kazhikhov, On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscosity fluid, Siberian Math. J., 36 (1995), 1108-1141.
doi: 10.1007/BF02106835. |
[13] |
H. Y. Wen, L. Yao and C. J. Zhu, A blow-up criterion of strong solution to a 3D viscous liquid-gas two-phase flow model with vacuum, J.Math.Pures Appl., 97 (2012), 204-229.
doi: 10.1016/j.matpur.2011.09.005. |
[14] |
H. Y. Wen and C. J. Zhu, Blow-up criterions of strong solutions to 3D compressible Navier-Stokes equations with vacuum, Advances in Mathematics, 248 (2013), 534-572.
doi: 10.1016/j.aim.2013.07.018. |
[15] |
L. Yao and C. J. Zhu, Free boundary value problem for a viscous two-phase model with mass-dependent viscosity, J. Differential Equations, 247 (2009), 2705-2739.
doi: 10.1016/j.jde.2009.07.013. |
[16] |
L. Yao and C. J. Zhu, Existence and uniqueness of global weak solution to a two-phase flow model with vacuum, Math. Ann., 349 (2011), 903-928.
doi: 10.1007/s00208-010-0544-0. |
[17] |
L. Yao, T. Zhang and C. J. Zhu, Existence and asymptotic behavior of global weak solutions to a 2D viscous liquid-gas two-phase flow model, SIAM J. Math. Anal., 42 (2010), 1874-1897.
doi: 10.1137/100785302. |
[18] |
L. Yao, T. Zhang and C. J. Zhu, A blow-up criterion for a 2D viscous liquid-gas two-phase flow model, J. Differential Equations, 250 (2011), 3362-3378.
doi: 10.1016/j.jde.2010.12.006. |
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