Space-time behavior for radiative hydrodynamics model with or without heat conduction
DOI:
https://doi.org/10.58997/ejde.2023.60Keywords:
Green's function; radiative hydrodynamics model; space-time estimateAbstract
We consider space-time behaviors of smooth solutions for the radiative hydrodynamics system with or without heat conduction in the whole space \(R^3\) by using Green's function method. This result exhibits the generalized Huygens' principle as the classical compressible Navier-Stokes equations [3,26], which is different from the Hamer model for radiating gases in [36].
For more information see https://ejde.math.txstate.edu/Volumes/2023/60/abstr.html
References
S. J. Deng, S. H. Yu; Greens function and pointwise convergence for compressible Navier- Stokes equations, Quart. Appl. Math., 75 (3)(2017), 433-503.
S. J. Deng, X .F. Yang; Pointwise structure of a radiation hydrodynamic model in onedimension, Math. Methods Appl. Sci., 43 (6)(2020), 3432-3456.
L. L. Du, Z. G. Wu; Solving the non-isentropic Navier-Stokes equations in odd space dimensions: The Green function method, J. Math. Phys., 58(10)(2017), 101506.
R. J. Duan, K. Fellner, C. J. Zhu; Energy method for multidimensional balance laws with non-local dissipation, Journal of de MathŽematiques Pures et AppliqŽes, 93 (2010), 572-598.
L. L. Fan, L. Z. Ruan, W. Xiang; Asymptotic stability of a composite wave of two viscous shock waves for the one-dimensional radiative Euler equations, Ann. Inst. Henri Poincare, Anal. Non LinŽeaire, 36 (1)(2019), 1-25.
M. di Francesco; Initial value problem and relaxation limits of the Hamer model for radiating gases in several space variables, NoDEA Nonlinear Differ. Equ. Appl., 13 (5-6)(2007), 531- 562.
W. Gao, C. Zhu; Asymptotic decay toward the planar rarefaction waves for a model system of the radiating gas in two dimensions, Math. Models Methods Appl. Sci., 18 (4)(2008), 511-541.
W. Gao, L. Ruan, C. Zhu; Decay rates to the planar rarefaction waves for a model system of the radiating gas in n dimensions, J. Diff. Eqns., 244 (10)(2008), 2614-2640.
G. Q. Gong, J. W. Zhou, B. R. Zhu; Global existence and optimal decay rate of the classical solution to 3-D radiative hydrodynamics model with or without heat conductivity, J. Diff. Eqns., 343(2023), 718-751.
K. Hamer; Nonlinear effects on the propagation of sound waves in a radiating gas, Quarterly Journal of Mechanics and Applied Mathematics, 24 (1971), 155-168.
D. Hoff, K. Zumbrun; Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow, Indiana Univ. Math. J., 44 (2)(1995), 603-676.
D. Hoff, K. Zumbrun; Pointwise decay estimates for multidimensional Navier-Stokes diffusion waves, Z. angew. Math. Phys., 48 (1997), 597-614.
H. Hong; Asymptotic behavior toward the combination of contact discontinuity with rarefaction waves for 1-D compressible viscous gas with radiation, Nonlinear Anal. (Real World Appl.), 35 (2017), 175-199.
B. Huang, L. Zhang; Asymptotic stability of planar rarefaction wave to 3D radiative hydrodynamics, Nonlinear Anal. (Real World Appl.), 46 (2019), 43-57.
S. Kawashima, Y. Nikkuni, S. Nishibata; The initial value problem for hyperbolic-elliptic coupled systems and applicationsto radiation hydrodynamics, in: Analysis of Systems of Conservation Laws, Aachen, 1997, in: Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math., vol. 99, Chapman & Hall/CRC, Boca Raton, FL, 1999, 87-127.
S. Kawashima, Y. Nikkuni, S. Nishibata; Large-time behavior of solutions to hyperbolicelliptic coupled systems, Arch. Ration. Mech. Anal., 170(4)(2003), 297-329.
L. He, Y. Liao, T. Wang, H. Zhao; One-dimensional viscous radiative gas with temperature dependent viscosity, Acta Math. Sci. Ser. B (Engl. Ser.), 38 (2018), 15151548.
C. Lattanzio, C. Mascia, D. Serre; Shock waves for radiative hyperbolic-elliptic systems, Indiana Univ. Math. J., 56(5)(2007), 2601-2640.
S. Li, J. Wang; Formation of singularities of solutions to a 1D compressible radiation hydrodynamics model, Nonlinear Anal., 222 (2022), 112969.
D. L. Li; The Greens function of the Navier-Stokes equations for gas dynamics in R3, Commun. Math. Phys., 257(2005), 579-619.
Y. Liao, H. Zhao; Global existence and large-time behavior of solutions to the Cauchy problem of one-dimensional viscous radiative and reactive gas, J. Diff. Eqns., 265 (2018), 2076-2120.
C. Lin; Asymptotic stability of rarefaction waves in radiative hydrodynamics, Commun. Math. Sci., 9(1)(2011), 207-223.
C. Lin, T. Goudon; Global existence of the equilibrium diffusion model in radiative hydrodynamics, Chin. Ann. Math., Ser. B, 32 (4)(2011), 549-568.
C. Lin, J.-F. Coulombel, T. Goudon; Asymptotic stability of shock profiles in radiative hydrodynamics, C. R. Math. Acad. Sci. Paris, 345(11)(2007), 625-628.
T. P. Liu, S. E. Noh; Wave propagation for the compressible Navier-Stokes equations, J. Hyperbolic Differ. Equ., 12 (2015), 385-445.
T. P. Liu, W. K. Wang; The pointwise estimates of diffusion wave for the Navier-Stokes systems in odd multi-dimension, Comm. Math. Phys., 196(1998), 145-173.
T. P. Liu, Y. N. Zeng; Large time behavior of solutions for general quasilinear hyperbolicparabolic systems of conservation laws, Mem. Amer. Math. Soc., 125 (1997).
S. Nishibata; Asymptotic behavior of solutions to a model system of a radiating gas with discontinuous initial data, Mathematical Models and Methods in Applied Sciences, 10 (2000), 1209-1231.
M. Nishikawa, S. Nishibata; Convergence rates toward the travelling waves for a model system of the radiating gas, Math. Methods Appl. Sci., 30 (2007), 649-663.
C. Rohde, W. Wang, F. Xie; Hyperbolic-hyperbolic relaxation limit for a 1D compressible radiation hydrodynamics model: superposition of rarefaction and contact waves, Commun. Pure Appl. Anal., 12 (5)(2013), 2145-2171.
L. Z. Ruan, C. J. Zhu; Asymptotic decay toward rarefaction wave for a hyperbolic-elliptic coupled system on half space, J. Partial Diff. Eqns., 21 (2008), 173-192.
D. Serre; L1-stability of constants in a model for radiating gases, Communications in Mathematical Sciences, 1(2003), 197-205.
L. Wan, L. X. Wu; Global symmetric solutions for a multi-dimensional compressible viscous gas with radiation in exterior domains, Z. Angew. Math. Phys., 70 (4)(2019), 130.
J. Wang, F. Xie; Asymptotic stability of viscous contact wave for the 1D radiation hydrodynamics system, J. Diff. Eqns., 251(4-5)(2011), 1030-1055.
W. Wang, F. Xie; The initial value problem for a multi-dimensional radiation hydrodynamics model with viscosity, Math. Methods Appl. Sci., 34 (7)(2011), 776-791.
W. K. Wang, W. J. Wang; The pointwise estimates of solutions for a model system of the radiating gas in multi-dimensions, Nonlinear Anal., 71 (3-4)(2009), 1180-1195.
W. K. Wang, Z. G. Wu; Pointwise estimates of solution for the Navier-Stokes-Poisson equations in multi-dimensions, J. Diff. Eqns., 248 (2010), 1617-1636.
W. K. Wang, T. Yang; The pointwise estimates of solutions for Euler equations with damping in multi-dimensions, J. Diff. Eqns., 173 (2001), 410-450.
Z. G. Wu, W. K. Wang; Pointwise estimates of solution for non-isentropic Navier-Stokes- Poisson equations in multi-dimensions, Acta Math. Sci., 32B (5)(2012), 1681-1702.
Z. G. Wu, W. K. Wang; Pointwise estimates for bipolar compressible Navier-Stokes-Poisson system in dimension three, Arch. Rational Mech. Anal., 226 (2)(2017), 587-638.
Z. G. Wu, W. K. Wang; Generalized Huygens principle for bipolar non-isentropic compressible Navier-Stokes-Poisson system in dimension three, J. Diff. Eqns., 269 (10)(2020), 7906-7930.
F. Xie; Nonlinear stability of combination of viscous contact wave with rarefaction waves for a 1D radiation hydrodynamics model, Discrete Contin. Dyn. Syst., 17 (3)(2012), 1075-1100.
Y. N. Zeng; L1 Asymptotic behavior of compressible isentropic viscous 1-D flow, Comm. Pure Appl. Math., 47 (1994), 1053-1082.
Downloads
Published
License
Copyright (c) 2023 Mengqian Liu, Zhigang Wu
This work is licensed under a Creative Commons Attribution 4.0 International License.
