Asymptotic limits of the Euler–Poisson equations for dissipative measure-valued solutions

References

• Degond P. Mathematical modeling of microelectronics semiconductor devices, some current topics on nonlinear conservation laws. AMS/IP Stud. Adv. Math. vol. 15; Providence (RI): Amer. Math. Soc.; 2000. p. 77–110.
   Google Scholar
• Cordier S, Grenier E. Quasineutral limit of an Euler-Poisson system arising from plasma physics. Comm Partial Differ Equ. 2000;25(5–6):1099–1113.
   Web of Science ®Google Scholar
• Wang S. Quasineutral limit of Euler-Poisson system with and without viscosity. Comm Partial Differ Equ. 2005;29(3–4):419–456.
   Web of Science ®Google Scholar
• Loeper G. Quasi-neutral limit of the Euler-Poisson and Euler-Monge-Ampe‘re systems. Comm Partial Differ Equ. 2005;30(8):1141–1167.
   Web of Science ®Google Scholar
• Peng YJ, Wang YG, Yong WA. Quasi-neutral limit of the non-isentropic Euler-Poisson system. Proc R Soc Edin A. 2006;136(5):1013–1026.
   Google Scholar
• Li YP. Convergence of the nonisentropic Euler-Poisson equations to incompressible type Euler equations. J Math Anal Appl. 2008;342(2):1107–1125.
   Web of Science ®Google Scholar
• Jiang S, Ju QC, Li HL, et al. Quasi-neutral limit of the full bipolar Euler-Poisson system. Sci China Math. 2010;53(12):3099–3114.
   Web of Science ®Google Scholar
• Pu XK. Quasineutral limit of the pressureless Euler-Poisson equation. Appl Math Lett. 2014;30:33–37.
   Web of Science ®Google Scholar
• Ju QC, Li FC, Li HL. The quasineutral limit of compressible Navier-Stokes-Poisson system with heat conductivity and general initial data. J Differ Equ. 2009;247(1):203–224.
   Web of Science ®Google Scholar
• Brenier Y. Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Comm Partial Differ Equ. 2000;25(3–4):737–754.
   Web of Science ®Google Scholar
• Masmoudi N. From Vlasov-Poisson system to the incompressible Euler system. Comm Partial Differ Equ. 2001;26(9–10):1913–1928.
   Web of Science ®Google Scholar
• Jüngel A, Peng YJ. A hierarchy of hydrodynamic models for plasmas: quasi-neutral limits in the drift-diffusion equations. Asympt Anal. 2001;28:49–73.
   Web of Science ®Google Scholar
• Li HL, Lin CK. Zero Debye length asymptotic of the quantum hydrodynamic model for semiconductors. Comm Math Phys. 2005;256(1):195–212.
   Web of Science ®Google Scholar
• Gasser I, Marcati P. The combined relaxation and vanishing Debye length limit in the hydrodynamic model for semiconductors. Math Methods Appl Sci. 2001;24:81–92.
   Web of Science ®Google Scholar
• Jiang S, Wang S. The convergence of the Navier-Stokes-Poisson system to the incompressible Euler equations. Comm Partial Differ Equ. 2005;31:571–591.
   Web of Science ®Google Scholar
• Donatelli D, Marcati P. A quasineutral type limit for the Navier-Stokes-Poisson system with large data. Nonlinearity. 2008;21(1):135–148.
   Web of Science ®Google Scholar
• Demoulini S, Stuart D, Tzavaras A. Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics. Arch Ration Mech Anal. 2012;205(3):927–961.
   Web of Science ®Google Scholar
• Feireisl E, Gwiazda P, Świerczewska-Gwiazda A, et al. Dissipative measure-valued solutions to the compressible Navier-Stokes system. Calc Var Partial Differ Equ. 2016;55(6):Article ID 141, 20 pp.
   Web of Science ®Google Scholar
• Gwiazda P, Swierczewska-Gwiazda A, Wiedemann E. Weak-strong uniqueness for measure-valued solutions of some compressible fluid models. Nonlinearity. 2015;28(11):3873–3890.
   Web of Science ®Google Scholar
• Feireisl E, Klingenberg C, Markfelder S. On the low Mach number limit for the compressible Euler system. SIAM J Math Anal. 2019;51(2):1496–1513.
   Web of Science ®Google Scholar
• Feireisl E, Tang T. On a singular limit for the stratified compressible Euler system. Asymptot Anal. 2019;14:59–72.
   Google Scholar
• Nečsová Š, Tang T. On a singular limit for the compressible rotating Euler system. J Math Fluid Mech. 2020;22(3):43.
   Web of Science ®Google Scholar
• Alibert JJ, Bouchitté G. Non-uniform integrability and generalized Young measures. J Convex Anal. 1997;4:129–147.
   Google Scholar
• Málek J, Nečas J, Rokyta M, et al. Weak and measure-valued solutions to evolutionary PDE's. London: Chapman and Hall; 1996.
   Google Scholar
• Neustupa J. Measure-valued solutions of the Euler and Navier-Stokes equations for compressible barotropic fluids. Math Nachr. 1993;163(1):217–227.
   Google Scholar
• Kato T. Nonstationary flows of viscous and ideal fluids in R3. J Funct Anal. 1972;9(3):296–305.
   Google Scholar
• Kato T, Lai CY. Nonlinear evolution equations and the Euler flow. J Funct Anal. 1984;56(1):15–28.
   Web of Science ®Google Scholar
• Lions PL, Masmoudi N. Incompressible limit for a viscous compressible fluid. J Math Pures Appl. 1998;77(6):585–627.
   Web of Science ®Google Scholar