Global Existence of Smooth Solutions for a Nonconservative Bitemperature Euler Model

The bitemperature Euler model describes a crucial step of inertial confinement fusion (ICF) when the plasma is quasineutral while ionic and electronic temperatures remain distinct. The model is wri...

[1]  G. Carbou,et al.  Semilinear behavior for totally linearly degenerate hyperbolic systems with relaxation. , 2009 .

[2]  Shuichi Kawashima,et al.  Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation , 1985 .

[3]  Jérôme Breil,et al.  Modelling and numerical approximation for the nonconservative bitemperature Euler model , 2018, ESAIM: Mathematical Modelling and Numerical Analysis.

[4]  S. Kawashima,et al.  Global existence and optimal decay rates for the Timoshenko system: The case of equal wave speeds , 2014, 1407.4975.

[5]  Thomas C. Sideris,et al.  Formation of singularities in three-dimensional compressible fluids , 1985 .

[6]  R. Natalini,et al.  On Relaxation Hyperbolic Systems Violating the Shizuta–Kawashima Condition , 2010 .

[7]  Yanjin Wang,et al.  Global classical solutions to partially dissipative hyperbolic systems violating the Kawashima condition , 2015, 1508.02867.

[8]  Yanni Zeng,et al.  Gas Dynamics in Thermal Nonequilibrium¶and General Hyperbolic Systems¶with Relaxation , 1999 .

[9]  Roberto Natalini,et al.  GLOBAL EXISTENCE OF SMOOTH SOLUTIONS FOR PARTIALLYDISSIPATIVE HYPERBOLIC SYSTEMS WITH A CONVEX ENTROPYB , 2002 .

[10]  Tosio Kato,et al.  The Cauchy problem for quasi-linear symmetric hyperbolic systems , 1975 .

[11]  Yue-Jun Peng,et al.  Uniform global existence and parabolic limit for partially dissipative hyperbolic systems , 2016 .

[12]  Yue-Jun Peng Euler–Lagrange change of variables in conservation laws , 2007 .

[13]  B. Dubroca,et al.  A kinetic approach of the bi-temperature Euler model , 2020 .

[14]  Peter D. Lax,et al.  Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations , 1964 .

[15]  David H. Wagner,et al.  Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions , 1987 .

[16]  Shu Wang,et al.  Relaxation Limit and Global Existence of Smooth Solutions of Compressible Euler-Maxwell Equations , 2011, SIAM J. Math. Anal..

[18]  Thomas C. Sideris,et al.  Long Time Behavior of Solutions to the 3D Compressible Euler Equations with Damping , 2003 .

[19]  Wen-An Yong,et al.  Entropy and Global Existence for Hyperbolic Balance Laws , 2004 .