CRITICAL THRESHOLDS

A collection of selected references on

Critical thresholds in the regularity of Eulerian dynamics.




  • S. Schochet and E. Tadmor
    Regularized Chapman-Enskog expansion for scalar conservation laws
    Archive for Rational Mechanics and Analysis 119 (1992) 95-107.

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  • M. Grassin
    Existence of global smooth solutions to Euler equations for an isentropic perfect gas
    Indiana Univ. Math. Journal. 47(2) (1998) 1397-1432.

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  • S. Engelberg, H. Liu and E. Tadmor
    Critical thresholds in Euler-Poisson equations
    Indiana University Math journal 50(1) (2001) 109-157.

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  • H. Liu and E. Tadmor
    Critical thresholds in a convolution model for nonlinear conservation laws
    SIAM Journal on Mathematical Analysis 33(4) (2001) 930-945.

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  • H. Liu and E. Tadmor
    Spectral dynamics of the velocity gradient field in restricted flows
    Communications in Mathematical Physics 228 (2002) 435-466.

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  • H. Liu and E. Tadmor
    Semi-classical limit of the nonlinear Schrödinger-Poisson equation with sub-critical initial data
    Methods and Applications in Analysis 9(4) (2002) 517-532.

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  • P. Godin
    A class of global non-smooth axisymmetric solutions to the Euler equations of an isentropic perfect gas in 2 space dimensions
    in "Hyperbolic Problems: Theory, Numerics, Applications", 9th International Conference on Hyperbolic Problems held in Pasadena in 2002 (T. Hou and E Tadmor eds.), Springer (2003) 549-555..

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  • H. Liu and E. Tadmor
    Critical thresholds and conditional stability for Euler equations and related models
    in "Hyperbolic Problems: Theory, Numerics, Applications", 9th International Conference on Hyperbolic Problems held in Pasadena in 2002 (T. Hou and E. Tadmor, eds.), Springer (2003) 227-240..

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  • H. Liu and E. Tadmor
    Critical thresholds in 2D restricted Euler-Poisson equations
    SIAM Journal of Applied Mathematics 63(6) (2003) 1889-1910..

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  • H. Liu and E. Tadmor
    Rotation prevents finite-time breakdown
    Physica D 188 (2004) 262-276.

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  • H. Liu
    Critical thresholds in the semiclassical limit of 2-D rotational Schrodinger equations
    ZAMP 57 (2006) 42-58.

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  • H. Liu
    Global orientation dynamics for liquid crystalline polymers
    Physica D 228 (2007) 122-129.

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  • B. Cheng and E.Tadmor
    Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations
    SIAM Journal on Mathematical Analysis 39(5) (2008) 1668-1685.

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  • T. Li and H. Liu
    Critical thresholds in a relaxation model for travel flows
    Indiana Univ. Math. Journal 57(3) (2008) 1409-1430.

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  • E. Tadmor and D. Wei
    On the global regularity of sub-critical Euler-Poisson equations with pressure
    Journal of the European Mathematical Society 10 (2008) 757-769.

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  • D. Chae and E. Tadmor
    On the finite time blow-up of the Euler-Poisson equations in Rn
    Communications in Mathematical Sciences 6(3) (2008) 785-789.

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  • T. Li and H. Liu
    Critical thresholds in hyperbolic relaxation systems
    Journal of Differential Equations 247(1) (2009) 33-48.

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  • T. Li and H. Liu
    Critical thresholds in a relaxation system with resonance of characteristic speeds
    Discrete and Continuous Dynamical Systems - Series A 24(2) (2009) 51--521.

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  • B. Cheng and E. Tadmor
    An improved local blow-up condition for Euler-Poisson equations with attractive forcing
    Physica D 238 (2009) 2062-2066.

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  • Tong Li and Sunčica Čanić
    Critical thresholds in a quasilinear hyperbolic model of blood flow
    Networks and Heterogeneous Media 4(3) (2009) 527-536.

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  • H. Liu, E. Tadmor and D. Wei
    Global regularity of the 4D Restricted Euler Equations
    Physica D 239 (2010) 1225-1231.

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  • D. Wei
    Critical thresholds in multi-dimensional restricted Euler equations
    Communications in Mathematical Sciences 9(2) (2011) 583-596.

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  • Bin Cheng and Chunjing Xie
    On the classical solutions of two dimensional inviscid rotating shallow water system
    J. Differential Equations 250 (2011) 690-709.

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  • D. Wei, E. Tadmor and H. Bae
    Critical thresholds in multi-dimensional Euler-Poisson equations with radial symmetry
    Communications in Mathematical Sciences 10(1) (2012) 75-86.

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  • J. Hunter and M. Ifrim
    Quasi-linear Schrödinger equation for large amplitude inertial oscillations in a rotating shallow fluid
    IMA Journal of Applied Mathematics (2013).

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  • Y. Lee and H. Liu
    Thresholds in three-dimensional restricted Euler-Poisson equations
    Physica D 262 (2013) 59-70.

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  • Yongki Lee and Hailiang Liu
    Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics.

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  • E. Tadmor and C. Tan
    Critical thresholds in flocking hydrodynamics with nonlocal alignment.

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