\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Global well posedness for the ghost effect system

Abstract Full Text(HTML) Related Papers Cited by
  • The aim of this paper is to discuss the issue of global existence of weak solutions of the so called ghost effect system which has been derived recently in [C. D. LEVERMORE, W. SUN, K. TRIVISA, SIAM J. Math. Anal. 2012]. We extend the local existence of solutions proved in [C.D. LEVERMORE, W. SUN, K. TRIVISA, Indiana Univ. J., 2011] to a global existence result. The key tool in this paper is a new functional inequality inspired of what proposed in [A. JÜNGEL, D. MATTHES, SIAM J. Math. Anal., 2008]. Such an inequality being adapted in [D. BRESCH, A. VASSEUR, C. YU, 2016] to be useful for compressible Navier-Stokes equations with degenerate viscosities. Our strategy to prove the global existence of solution builds upon the framework developed in [D. BRESCH, V. GIOVANGILI, E. ZATORSKA, J. Math. Pures Appl., 2015] for low Mach number system.

    Mathematics Subject Classification: 35G25, 35Q30, 35Q40, 35D30, 82D05, 82D37.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] P. Antonelli and S. Spirito, A global existence result for a zero mach number system, arXiv: 1605.03510, 2016.
    [2] D. Bresch, F. Couderc, P. Noble and J. -P. Vila, New extended formulations of euler-korteweg equations based on a generalization of the quantum bohm identity, arXiv: 1503.08678, 2015.
    [3]

    D. Bresch, B. Desjardins and E. Zatorska, Two-velocity hydrodynamics in fluid mechanics: Part ii existence of global κ-entropy solutions to the compressible navier-stokes systems with degenerate viscosities, J. Math. Pures Appl., 4 (2015), 801-836.doi: 10.1016/j.matpur.2015.05.004.

    [4]

    D. Bresch, E. H. Essoufi and M. Sy, Effect of density dependent viscosities on multiphasic incompressible fluid models, Journal of Math. Fluid Mech., 3 (2007), 377-397.doi: 10.1007/s00021-005-0204-4.

    [5]

    D. Bresch, V. Giovangigli and E. Zatorska, Two-velocity hydrodynamics in fluid mechanics: Part i well posedness for zero mach number systems, Journal de Math. Pures. Appl., 4 (2015), 762-800.doi: 10.1016/j.matpur.2015.05.003.

    [6] D. Bresch, A. Vasseur and C. Yu, Global existence of compressible Navier-Stokes equation with degenerates viscosities, In preparation, (2016).
    [7]

    R. Danchin and X. Liao, On the well-posedness of the full low Mach number limit system in general critical Besov spaces, Commun. Contemp. Math., 3 (2012), 125-0022.doi: 10.1142/S0219199712500228.

    [8]

    J. Dong, A note on barotropic compressible quantum Navier-Stokes equations, Nonlinear Anal., 4 (2010), 854-856.doi: 10.1016/j.na.2010.03.047.

    [9] M. Gisclon and I. Lacroix-Violet, About the barotropic compressible quantum Navier-Stokes equations, Nonlinear Anal. , (2015), 106-121. doi: 10.1016/j.na.2015.07.006.
    [10]

    F. Jiang, A remark on weak solutions to the barotropic compressible quantum Navier-Stokes equations, Nonlinear Anal. Real World Appl., 3 (2011), 1733-1735.doi: 10.1016/j.nonrwa.2010.11.005.

    [11]

    A. Jüngel, Global weak solutions to compressible navier-stokes equations for quantum fluids, SIAM J. Math. Anal., 3 (2010), 1025-1045.doi: 10.1137/090776068.

    [12]

    A. Jüngel and D. Matthes, The derrida-lebowitz-speer-spohn equation: existence, nonuniqueness, and decay rates of the solutions, SIAM J. Math. Anal., 6 (2008), 1996-2015.doi: 10.1137/060676878.

    [13]

    C. D. Levermore, W. Sun and K. Trivisa, A low mach number limit of a dispersive navierstokes system, SIAM J. Math. Anal., 3 (2012), 1760-1807.doi: 10.1137/100818765.

    [14]

    C. D. Levermore, W. R. Sun and K. Trivisa, Local well-posedness of a ghost effect system, Indiana Univ. Math. J., 2 (2009), 517-576.

    [15]

    X. Liao, A global existence result for a zero Mach number system, J. Math. Fluid Mech., 1 (2014), 77-103.doi: 10.1007/s00021-013-0152-3.

    [16] P. -L. Lions, Mathematical Topics in Fluid Mechanics. Vol. 1. Incompressible Models, Oxford Lecture Series in Mathematics and its Applications, The Clarendon Press, Oxford University Press, New York, 1996.
    [17] P. -L Lions, Mathematical Topics in Fluid Mechanics. Vol. 2 Compressible Models, Oxford Lecture Series in Mathematics and its Applications. The Clarendon Press, Oxford University Press, New York, 1998.
    [18] J. -C. Maxwell, On stresses in rarified gases arising from inequalities of temperature, Philos Trans R Soc Lond B Biol Sci, (1879), 231-256.
    [19]

    J. Simon, On the existence of the pressure for solutions of the variational Navier-Stokes equations, J. Math. Fluid Mech., 3 (1999), 225-234.doi: 10.1007/s000210050010.

    [20]

    Y. Sone, Flows induced by temperature fields in a rarefied gas and their ghost effect on the behavior of a gas in the continuum limit, Annu. Rev. Fluid Mech., 32 (2000), 779-811.doi: 10.1146/annurev.fluid.32.1.779.

    [21] Y. Sone, Kinetic Theory and Fluid Dynamics, Birkhäuser Boston, Inc. , Boston, MA, 2002. doi: 10.1007/978-1-4612-0061-1.
    [22] C. Villani, A review of mathematical topics in collisional kinetic theory, Handbook of mathematical fluid dynamics, Vol. Ⅰ (2002), 71-305. doi: 10.1016/S1874-5792(02)80004-0.
  • 加载中
SHARE

Article Metrics

HTML views(1233) PDF downloads(152) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return