[1] Anile A M. An extended thermodynamic framework for the hydrodynamical modeling of semiconductors. Pitman Research Notes In
Mathematics Series, 1995, 340: 3--41
[2] Cerignani C. The Boltzmann equation and its applications//Applied Mathematical Sciences. New York: Springer-Valag, 1988
[3] Cercignani C, Illner R, Pulvirenti M. The mathematical theory of dilute gases//Applied Mathematical Sciences. New York: Springer-Verlag, 1994
[4] Choe H J, Kim H. Strong solutions of the Navier-Stokes equations for isentropic compressible fluids. J Differential Equations, 2003, 190: 504--523
[5] Gerasimenko V I, Petrina Y D. The Boltzmann-Grad limit theorem (Russian). Dokl Akad Nauk Ukrain SSR Ser A, 1989, 11: 12--16
[6] Kobayashi P T, Suzuki T. Weak solutions to the Navier-Stokes-Poisson equations. Preprint, 2004
[7] Lions P L. Mathematical Topics in Fluid Dynamics, Vol.2, Compressible Models. Oxford: Oxford Science Publication, 1998
[8] Marcati P, Natalini R. Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation. Arch
Rational Mech Anal, 1995, 129: 129--145
[9] Marcati P, Natalini R. Weak solutions to a hydrodynamic model for semiconductors: the Cauchy problem. Proc Soc Edinburgh Sect A,
1995, 125(1): 115--131
[10] Markowich P A. The Steady-State Semiconductor Device Equations. New York: Springer-Verlag, 1986
[11] Markowich P A, Ringhofer C, Schmeiser C. Semiconductor Equations. New York: Springer-Verlag, 1990
[12] Matsusu-Necasova S, Okada M, Makino T. Free boundary problem for the equation of spherically symmetric motion of viscous gas
(II). Japan J Indust Appl Math, 1995, 12: 195--203
[13] Matsusu-Necasova S, Okada M, Makino T. Free boundary problem for the equation of spherically symmetric motion of viscous gas
(III). Japan J Indust Appl Math, 1997, 14: 199--213
[14] Makino T, Okada M. Free boundary problem for the equation of spherically symmetric motion of viscous gas. Japan J Indust Appl Math, 1993, 10(2): 219--235
[15] Simon J. Nonhomogeneous viscous incompressible fluids: existence of velocity, density, and pressure. SIAM J Math Anal, 1990, 21(5): 1093--1117
[16] Ukai S. The Boltzmann-Grad limit and Cauchy-Kovalevskaya theorem, Recent topics in mathematics moving toward science and
engineering. Japan J Indust Appl Math, 2001, 18(2): 383--392
[17] Valli A. Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method. Ann Sc Norm Super
Pisa Cl Sci, 1983, 10(4): 607--647
[18] Zhang Y H, Tan Z. On the existence of solutions to the Navier-Stokes-Poisson equations of a two-dimensional compressible flow. Math Methods Appl Sci, 2007, 30(3): 305--329 |