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Liu, Jian; Lian, Ruxu

Global existence of the cylindrically symmetric strong solution to compressible Navier-Stokes equations. (English) Zbl 1474.35535

Abstr. Appl. Anal. 2014, Article ID 728715, 8 p. (2014).
Summary: This paper is concerned with the initial boundary value problem for the three-dimensional Navier-Stokes equations with density-dependent viscosity. The cylindrically symmetric strong solution is shown to exist globally in time and tend to the equilibrium state exponentially as time grows up.

Cited in 2 Documents

MSC:

35Q35 PDEs in connection with fluid mechanics
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35D35 Strong solutions to PDEs
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\textit{J. Liu} and \textit{R. Lian}, Abstr. Appl. Anal. 2014, Article ID 728715, 8 p. (2014; Zbl 1474.35535)
Full Text: DOI

References:

[1] Gerbeau, J. F.; Perthame, B., Derivation of viscous Saint-Venant system for laminar shallow water, numerical validation, Discrete and Continuous Dynamical Systems B, 1, 1, 89-102 (2001) · Zbl 0997.76023
[2] Marche, F., Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects, European Journal of Mechanics—B/Fluids, 26, 1, 49-63 (2007) · Zbl 1105.76021
[3] Bresch, D.; Desjardins, B., Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model, Communications in Mathematical Physics, 238, 1-2, 211-223 (2003) · Zbl 1037.76012
[4] Bresch, D.; Desjardins, B., On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier-Stokes models, Journal de Mathématiques Pures et Appliquées, 86, 4, 362-368 (2006) · Zbl 1121.35094
[5] Fang, D.; Zhang, T., Global solutions of the Navier-Stokes equations for compressible flow with density-dependent viscosity and discontinuous initial data, Journal of Differential Equations, 222, 1, 63-94 (2006) · Zbl 1357.35245
[6] Mellet, A.; Vasseur, A., Existence and uniqueness of global strong solutions for one-dimensional compressible Navier-Stokes equations, SIAM Journal on Mathematical Analysis, 39, 4, 1344-1365 (2008) · Zbl 1141.76054
[7] Li, H.-L.; Li, J.; Xin, Z.-P., Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations, Communications in Mathematical Physics, 281, 2, 401-444 (2008) · Zbl 1173.35099
[8] Danchin, R., Global existence in critical spaces for compressible Navier-Stokes equations, Inventiones Mathematicae, 141, 3, 579-614 (2000) · Zbl 0958.35100
[9] Feireisl, E.; Novotný, A.; Petzeltová, H., On the existence of globally defined weak solutions to the Navier-Stokes equations, Journal of Mathematical Fluid Mechanics, 3, 4, 358-392 (2001) · Zbl 0997.35043
[10] Huang, X. D.; Li, J.; Xin, Z. P., Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations, Communications on Pure and Applied Mathematics, 65, 4, 549-585 (2012) · Zbl 1234.35181
[11] Jiang, S.; Zhang, P., On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations, Communications in Mathematical Physics, 215, 3, 559-581 (2001) · Zbl 0980.35126
[12] Lions, P. L., Mathematical Topics in Fluid Mechanics. Mathematical Topics in Fluid Mechanics, Compressible Models, 2 (1998), New York, NY, USA: Oxford University Press, New York, NY, USA · Zbl 0908.76004
[13] Lian, R. X.; Liu, J.; Li, H. L.; Xiao, L., Cauchy problem for the one-dimensional compressible Navier-Stokes equations, Acta Mathematica Scientia B: English Edition, 32, 1, 315-324 (2012) · Zbl 1265.35031
[14] Frid, H.; Shelukhin, V., Boundary layers for the Navier-Stokes equations of compressible fluids, Communications in Mathematical Physics, 208, 2, 309-330 (1999) · Zbl 0946.35060
[15] Frid, H.; Shelukhin, V. V., Vanishing shear viscosity in the equations of compressible fluids for the flows with the cylinder symmetry, SIAM Journal on Mathematical Analysis, 31, 5, 1144-1156 (2000) · Zbl 0956.35102
[16] Fan, J.; Jiang, S., Zero shear viscosity limit for the Navier-Stokes equations of compressible isentropic fluids with cylindric symmetry, Rendiconti del Seminario Matematico Università e Politecnico di Torino, 65, 1, 35-52 (2007) · Zbl 1178.76307
[17] Jiang, S.; Zhang, J. W., Boundary layers for the Navier-Stokes equations of compressible heat-conducting flows with cylindrical symmetry, SIAM Journal on Mathematical Analysis, 41, 1, 237-268 (2009) · Zbl 1303.76117
[18] Yao, L.; Zhang, T.; Zhu, C., Boundary layers for compressible Navier-Stokes equations with density-dependent viscosity and cylindrical symmetry, Annales de l’Institut Henri Poincaré (C) Analyse Non Linéaire Articles, 28, 5, 677-709 (2011) · Zbl 1401.76118
[19] Guo, Z.; Li, H.-L.; Xin, Z., Lagrange structure and dynamics for solutions to the spherically symmetric compressible Navier-Stokes equations, Communications in Mathematical Physics, 309, 2, 371-412 (2012) · Zbl 1233.35156
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