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Strong solutions to compressible barotropic viscoelastic flow with vacuum
1. | Department of Mathematics, College of Sciences, Hohai University, Nanjing 210098, China |
2. | Department of Mathematics, Sichuan University, Chengdu, 610064, China |
References:
[1] |
Y. Cho, H. J. Choe and H. Kim, Unique solvability of the initial boundary value problems for compressible viscous fluids,, J. Math. Pures Appl., 83 (2004), 243.
doi: 10.1016/j.matpur.2003.11.004. |
[2] |
Y. M. Chu, X. G. Liu and X. Liu, Strong solutions to the compressible liquid crystal system,, Pacific J. Math., 257 (2012), 37.
doi: 10.2140/pjm.2012.257.37. |
[3] |
M. Hieber, Y. Naito and Y. Shibata, Global existence results for Oldroyd-B fluids in exterior domains,, J. Differential Equations, 252 (2012), 2617.
doi: 10.1016/j.jde.2011.09.001. |
[4] |
X. P. Hu and D. H. Wang, Local strong solution to the compressible viscoelastic flow with large data,, J. Differential Equations, 249 (2010), 1179.
doi: 10.1016/j.jde.2010.03.027. |
[5] |
X. P. Hu and D. H. Wang, Global existence for the multi-dimensional compressible viscoelastic flows,, J. Differential Equations, 250 (2011), 1200.
doi: 10.1016/j.jde.2010.10.017. |
[6] |
X. P. Hu and D. H. Wang, Strong solutions to the three-dimensional compressible viscoelastic fluids,, J. Differential Equations, 252 (2012), 4027.
doi: 10.1016/j.jde.2011.11.021. |
[7] |
C. Guillopé and J. C. Saut, Existence results for the flow of viscoelastic fluids with a differential constitutive law,, Nonlinear Anal., 15 (1990), 849.
doi: 10.1016/0362-546X(90)90097-Z. |
[8] |
X. D. Huang, J. Li and Z. P. Xin, Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations,, Comm. Pure Appl. Math., 65 (2012), 549.
doi: 10.1002/cpa.21382. |
[9] |
T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems,, Arch. Rational Mech. Anal., 58 (1975), 181.
doi: 10.1007/BF00280740. |
[10] |
R. Kupferman, C. Mangoubi and E. S. Titi, A Beale-Kato-Majda breakdown criterion for an Oldroyd-B fluid in the creeping flow regime,, Commun. Math. Sci., 6 (2008), 235.
doi: 10.4310/CMS.2008.v6.n1.a12. |
[11] |
P. D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves,, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, (1973).
|
[12] |
Z. Lei, C. Liu and Y. Zhou, Global solutions for incompressible viscoelastic fluids,, Arch. Ration. Mech. Anal., 188 (2008), 371.
doi: 10.1007/s00205-007-0089-x. |
[13] |
Z. Lei, C. Liu and Y. Zhou, Global existence for a 2D incompressible viscoelastic model with small strain,, Commun. Math. Sci., 5 (2007), 595.
doi: 10.4310/CMS.2007.v5.n3.a5. |
[14] |
F. Lin, C. Liu and P. Zhang, On hydrodynamics of viscoelastic fluids,, Comm. Pure Appl. Math., 58 (2005), 1437.
doi: 10.1002/cpa.20074. |
[15] |
F. Lin and P. Zhang, On the initial-boundary value problem of the incompressible viscoelastic fluid system,, Comm. Pure Appl. Math., 61 (2008), 539.
doi: 10.1002/cpa.20219. |
[16] |
P. L. Lions, Mathematical Topics in Fluid Mechanics,, vol. 2. Compressible Models, (1998).
|
[17] |
A. J. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables,, Applied Mathematical Sciences, (1984).
doi: 10.1007/978-1-4612-1116-7. |
[18] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases,, J. Math. Kyoto Univ., 20 (1980), 67.
|
[19] |
A. Matsumura and T. Nishida, Initial-boundary value problems for the equations of motion of compressible viscous and heat- conductive fluids,, Comm. Math. Phys., 89 (1983), 445.
doi: 10.1007/BF01214738. |
[20] |
J. G. Oldroyd, On the formation of rheological equations of state,, Proc. R. Soc. Lond. Ser. A, 200 (1950), 523.
doi: 10.1098/rspa.1950.0035. |
[21] |
J. G. Oldroyd, Non-Newtonian effects in steady motion of some idealized elastico-viscous liquids,, Proc. R. Soc. Lond. Ser. A, 245 (1958), 278.
doi: 10.1098/rspa.1958.0083. |
[22] |
J. Z. Qian and Z. F. Zhang, Global well-posedness for compressible viscoelastic fluids near equilibrium,, Arch. Ration. Mech. Anal., 198 (2010), 835.
doi: 10.1007/s00205-010-0351-5. |
[23] |
J. Z. Qian, Initial boundary value problems for the compressible viscoelastic fluid,, J. Differential Equations, 250 (2011), 848.
doi: 10.1016/j.jde.2010.07.026. |
[24] |
R. Salvi and I. Straškraba, Global existence for viscous compressible fluids and their behavior as $t\rightarrow\infty$,, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 40 (1993), 17.
|
show all references
References:
[1] |
Y. Cho, H. J. Choe and H. Kim, Unique solvability of the initial boundary value problems for compressible viscous fluids,, J. Math. Pures Appl., 83 (2004), 243.
doi: 10.1016/j.matpur.2003.11.004. |
[2] |
Y. M. Chu, X. G. Liu and X. Liu, Strong solutions to the compressible liquid crystal system,, Pacific J. Math., 257 (2012), 37.
doi: 10.2140/pjm.2012.257.37. |
[3] |
M. Hieber, Y. Naito and Y. Shibata, Global existence results for Oldroyd-B fluids in exterior domains,, J. Differential Equations, 252 (2012), 2617.
doi: 10.1016/j.jde.2011.09.001. |
[4] |
X. P. Hu and D. H. Wang, Local strong solution to the compressible viscoelastic flow with large data,, J. Differential Equations, 249 (2010), 1179.
doi: 10.1016/j.jde.2010.03.027. |
[5] |
X. P. Hu and D. H. Wang, Global existence for the multi-dimensional compressible viscoelastic flows,, J. Differential Equations, 250 (2011), 1200.
doi: 10.1016/j.jde.2010.10.017. |
[6] |
X. P. Hu and D. H. Wang, Strong solutions to the three-dimensional compressible viscoelastic fluids,, J. Differential Equations, 252 (2012), 4027.
doi: 10.1016/j.jde.2011.11.021. |
[7] |
C. Guillopé and J. C. Saut, Existence results for the flow of viscoelastic fluids with a differential constitutive law,, Nonlinear Anal., 15 (1990), 849.
doi: 10.1016/0362-546X(90)90097-Z. |
[8] |
X. D. Huang, J. Li and Z. P. Xin, Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations,, Comm. Pure Appl. Math., 65 (2012), 549.
doi: 10.1002/cpa.21382. |
[9] |
T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems,, Arch. Rational Mech. Anal., 58 (1975), 181.
doi: 10.1007/BF00280740. |
[10] |
R. Kupferman, C. Mangoubi and E. S. Titi, A Beale-Kato-Majda breakdown criterion for an Oldroyd-B fluid in the creeping flow regime,, Commun. Math. Sci., 6 (2008), 235.
doi: 10.4310/CMS.2008.v6.n1.a12. |
[11] |
P. D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves,, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, (1973).
|
[12] |
Z. Lei, C. Liu and Y. Zhou, Global solutions for incompressible viscoelastic fluids,, Arch. Ration. Mech. Anal., 188 (2008), 371.
doi: 10.1007/s00205-007-0089-x. |
[13] |
Z. Lei, C. Liu and Y. Zhou, Global existence for a 2D incompressible viscoelastic model with small strain,, Commun. Math. Sci., 5 (2007), 595.
doi: 10.4310/CMS.2007.v5.n3.a5. |
[14] |
F. Lin, C. Liu and P. Zhang, On hydrodynamics of viscoelastic fluids,, Comm. Pure Appl. Math., 58 (2005), 1437.
doi: 10.1002/cpa.20074. |
[15] |
F. Lin and P. Zhang, On the initial-boundary value problem of the incompressible viscoelastic fluid system,, Comm. Pure Appl. Math., 61 (2008), 539.
doi: 10.1002/cpa.20219. |
[16] |
P. L. Lions, Mathematical Topics in Fluid Mechanics,, vol. 2. Compressible Models, (1998).
|
[17] |
A. J. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables,, Applied Mathematical Sciences, (1984).
doi: 10.1007/978-1-4612-1116-7. |
[18] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases,, J. Math. Kyoto Univ., 20 (1980), 67.
|
[19] |
A. Matsumura and T. Nishida, Initial-boundary value problems for the equations of motion of compressible viscous and heat- conductive fluids,, Comm. Math. Phys., 89 (1983), 445.
doi: 10.1007/BF01214738. |
[20] |
J. G. Oldroyd, On the formation of rheological equations of state,, Proc. R. Soc. Lond. Ser. A, 200 (1950), 523.
doi: 10.1098/rspa.1950.0035. |
[21] |
J. G. Oldroyd, Non-Newtonian effects in steady motion of some idealized elastico-viscous liquids,, Proc. R. Soc. Lond. Ser. A, 245 (1958), 278.
doi: 10.1098/rspa.1958.0083. |
[22] |
J. Z. Qian and Z. F. Zhang, Global well-posedness for compressible viscoelastic fluids near equilibrium,, Arch. Ration. Mech. Anal., 198 (2010), 835.
doi: 10.1007/s00205-010-0351-5. |
[23] |
J. Z. Qian, Initial boundary value problems for the compressible viscoelastic fluid,, J. Differential Equations, 250 (2011), 848.
doi: 10.1016/j.jde.2010.07.026. |
[24] |
R. Salvi and I. Straškraba, Global existence for viscous compressible fluids and their behavior as $t\rightarrow\infty$,, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 40 (1993), 17.
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