河北师范大学学报—

期刊信息

刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
中国科技核心期刊
中国期刊方阵入选期刊
中国高校优秀科技期刊
华北优秀期刊
河北省优秀科技期刊

协同采编系统

友情链接

一维辐射流体力学方程组整体弱熵解的存在性

河海大学理学院, 江苏南京 211100
DOI： 10.13763/j.cnki.jhebnu.nse.2018.04.002

The Existence of Global Entropy Solutions to the One-dimensional Equations in Radiation Hydrodynamics

ZHOU Yulei, JIANG Peng

PDF
下载
HTML

摘要/Abstract

摘要：

证明了一维可压辐射流体力学方程组L^∞整体弱熵解的存在性.利用Godunov差分格式来构造近似解序列，并利用补偿列紧方法证明在包含真空以及任意大小初值的条件下该整体弱熵解的存在性.

Abstract：

We prove the existence of global entropy solutions in L^∞ to the one-dimensional compressible fluids in radiation hydrodynamics.The global weak entropy solutions are constructed using the Godunov finite difference scheme.The global existence of weak entropy solutions in L^∞ with arbitrarily large initial data even containing the vacuum is established with the aid of the compensated compactness method.

关键词

关键词： 辐射流体力学 ; 整体弱熵解 ; Godunov格式 ; 补偿列紧方法

Key words： radiation hydrodynamics ; global entropy solution ; Godunov scheme ; compensated compactness method

参考文献 20

[1] MIHALAS O,MIHALAS B W.Foundations of Radiation Hydrodynamics[M].New York:Oxford Univ Press,1984.
[2] POMRANING G C.The Equation of Radiation Hydrodynamics[M].New York:Pergamon Press,1973.
[3] KIPPENHAHN R,WEIGERT A.Stellar Structure and Evolution[M].Berlin-Heidelberg:Springer-verlag,1994.
[4] PENNER S S,OLFE D B.Radiation and Reentry[M].New York:Academic Press,1968.
[5] CHEN G Q.Convergence of Lax-friedrichs Scheme for Isentropic Gas Dynamics[J].Acta Math Sci,1986,6(4):75-120.doi:10.1016/s0252-9602(18)30535-6
[6] DING X,CHEN G Q,LOU P.Convergence of the Lax-friedrichs Scheme for Isentropic Gas Dynamics[J].Acta Math Sci,1985,5(4):415-472.doi:10.1016/s0252-9602(18)30543-5
[7] DING X,CHEN G Q,LOU P.Convergence of the Fraction Step Lax-friedrichs Scheme and Godunov Scheme for the Isentropic System of Gas Dynamics[J].Commun Math Phys,1989,121(1):63-84.doi:10.1007/BF01218624
[8] SVARD M.Entropy Solutions of the Compressible Euler Equations[J].Bit Numerical Mathematics,2016,56(4):1479-1496.doi:10.1007/s10543-016-0611-3
[9] BUGRA K.Existence of Undercompressive Weak Solutions to the Euler Equations[J].PAMM,2016,16(1):657-658.doi:10.1002/pamm.20160317
[10] HUANG F M,WANG Z.Convergence of Viscosity for Isothermal Gas Dynamics[J].Siam J Math Anal,2002,34(3):595-610.doi:10.1137/s0036141002405819
[11] MAKINO T,TAKENO S.Initial Boundary Value Problem for the Spherically Symmetric Motion of Isentropic Gas[J].Japan J Indust Appl Math,1994,11(1):173-183.doi:10.1007/BF03167220
[12] ZHANG B.Convergence of the Godunov Scheme for a Simplified One-dimensional Hydrodynamic Model for Semiconductor Devices[J].Commun Math Phys,1993,157(1):1-22.doi:10.1007/BF02098016
[13] JIU Quansen,LI Jun,NIU Dongjuan.Global Existence of Weak Solutions to the Three-dimensional Euler Equations with Helical Symmetry[J].Journal of Differential Equations,2017,262(10):5179-5205.doi:10.1016/j.jde.2017.01.019
[14] HU Yanbo.Axisymmetric Solutions of the Two-dimensional Euler Equations with a Two-constant Equation of State[J].Nonlinear Analysis:Real World Applications,2014,15(1):67-79.doi:10.1016/j.nonrwa.2013.06.001
[15] JIANG P,WANG D.Formation of Singularities of Solutions to the Three-dimensional Euler-boltzmann Equations in Radiation Hydrodynamics[J].Nonlinearity,2010,23(4):809-821.doi:10.1088/0951-7715/23/4/003
[16] JIANG S,ZHONG X H.Local Existence and Finite-time Blow-up in Multidimensional Radiation Hydrodynamics[J].J Math Fluid Mech,2007,9(4):543-564.doi:10.1007/s00021-005-0213-3
[17] KAWASHIMA S,NISHIBATA S.Cauchy Problem for a Model System of Radiaing Gas:Weak Solution with a Jump and Classical Solutions[J].Math Model Mech Appl Sci,1999,9(1):383-386.doi:10.1142/s0218202599000063
[18] KAWASHIMA S,NISHIBATA S.Shock Wave for a Model System of the Radiation Gas[J].Siam J Math Anal,1999,30(1):95-117.doi:10.1137/s0036141097322169
[19] LIONS P L,PERTHAME B,SOUGANISDIS E.Existence and Stability of Entropy Solutions for the Hyperbolic Systems of Isentropic Gas Dynamics in Eulerian and Lagrangian Coordinates[J].Comm Pure Appl Math,1996,49(6):599-638.doi:10.1002/(SICI)1097-0312(199606)49:6〈599::AIP-CPA2〉3.0.co:2-5
[20] LIONS P L,PERTHAME B,TADMOR E.Kinetic Formulation of the Isentropic Gas Dynamics and P-systems[J].Commun Math Phys,1994,163(2):415-431.doi:10.1007/BF02102014