Asymptotic stability of planar rarefaction wave to 3D radiative hydrodynamics

Huang, Bingkang; Zhang, Lan

doi:10.1016/j.nonrwa.2018.09.003

Cited by 9 publications

(7 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…|M 2 | ≤ q x (t) 2 + q(t) q x (t) v x (t) 2 ≤C(T ), and 20, we can deduce that to complete the proof of the a priori estimates stated in Lemma 2.2, we only need to get the positive lower bound of the absolute temperature θ(t, x) and this the main content of the next subsection.…”

Section: 2mentioning

confidence: 90%

Global Regularity for A Radiation Hydrodynamics Model with Viscosity and Thermal Conductivity

Zhang¹,

Zhao²

2022

Preprint

View full text Add to dashboard Cite

In this paper, we study the global wellposedness of a radiation hydrodynamics model with viscosity and thermal conductivity. It is now well-understood that, unlike the compressible Euler equations whose smooth solutions must blow up in finite time no matter how small and how smooth the initial data is, the dissipative structure of such a radiation hydrodynamics model can indeed guarantee that its one-dimensional Cauchy problem admits a unique global smooth solution provided that the initial data is sufficiently small, while for large initial data, even if the heat conductivity is taken into account but the viscosity effect is ignored, shock type singularities must appear in finite time for smooth solutions of the Cauchy problem of one-dimensional radiation hydrodynamics model with thermal conductivity and zero viscosity. Thus a natural question is, if effects of both the viscosity and the thermal conductivity are considered, does the one-dimensional radiation hydrodynamics model with viscosity and thermal conductivity exist a unique global large solution? We give affirmative answer to this problem and show in this paper that the initial-boundary value problem to the radiation hydrodynamics model in an one-dimensional periodic box T ∼ = R/Z with viscosity and thermal conductivity does exist a unique global smooth solution for any large initial data. The main ingredient in our analysis is to introduce some delicate estimates, especially an improved L m ([0, T ], L ∞ (T))−estimate on the absolute temperature for some m ∈ N and a pointwise estimate between the absolute temperature, the specific volume, and the first-order spatial derivative of the macro radiation flux, to deduce the desired positive lower and upper bounds on the density and the absolute temperature.

show abstract

Section: 2mentioning

confidence: 90%

Global Regularity for A Radiation Hydrodynamics Model with Viscosity and Thermal Conductivity

Zhang¹,

Zhao²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Now, we need to extend the local solution into a global solution. According to (22) and (23), there exists a -independent positive constant Γ 0 , such that…”

Section: Proposition 31 If the Initial Datamentioning

confidence: 99%

“…As for our model (1), we also refer to work of Hong, which has studied the the large time behavior toward the combination of two rarefaction waves and viscous contact wave for the Cauchy problem in one‐dimensional space, and work of Huang and Zhang, which has studied the large time behavior of the planar rarefaction wave for the Cauchy problem in three‐dimensional space.…”

Section: Introductionmentioning

confidence: 99%

“…The existence and asymptotic behavior of a unique classical solution to such a system have been proved in R 3 by Wang and Xie, 5 in which initial data are required to be small and the transport coefficients are supposed to be constants. As for our model (1), we also refer to work of Hong, 22 which has studied the the large time behavior toward the combination of two rarefaction waves and viscous contact wave for the Cauchy problem in one-dimensional space, and work of Huang and Zhang, 23 which has studied the large time behavior of the planar rarefaction wave for the Cauchy problem in three-dimensional space.…”

Section: Introductionmentioning

confidence: 99%

“…If X ⊂ R and Y is a Banach space, then C(X; Y ) denotes the space of continuous functions on X with values in Y ; L q (X; Y ) denotes the space of L q functions on X with values in Y , and || • || L q (X;Y ) denotes the norm of the space L q (X; Y ). We let C i (i ∈ N) denote some positive constants, which are independent of and only depend on Σ 0 and V 0 , where Σ 0 and V 0 are determined by (22) and (23). The symbol A ≲ B (or A ≳ B) means that A ≤ CB (or A ≥ CB) holds for some positive -independent constant C. To simplify the notation, we shall use…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global symmetric classical solutions for radiative compressible Navier‐Stokes equations with temperature‐dependent viscosity coefficients

Zhu

2020

Math Meth Appl Sci

View full text Add to dashboard Cite

This paper is concerned with the global solvability and the precise description of large time behavior of global solutions to the compressible viscous and heat‐conducting ideal polytropic gases in a bounded concentric annular domain with radiation and temperature‐dependent viscosity. For the case that the transport coefficients are smooth functions of temperature, a unique global‐in‐time spherically or cylindrically symmetric classical solution to the above initial‐boundary value problem is shown to exist and decay into a constant equilibrium state at exponential rate as the time variable tends to infinity. In our results, the initial data can be large if the adiabatic exponent is sufficiently close to 1.

show abstract

Global symmetric solutions for a multi-dimensional compressible viscous gas with radiation in exterior domains

Wan

2019

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

Asymptotic stability of planar rarefaction wave to 3D radiative hydrodynamics

Cited by 9 publications

References 24 publications

Global Regularity for A Radiation Hydrodynamics Model with Viscosity and Thermal Conductivity

Global Regularity for A Radiation Hydrodynamics Model with Viscosity and Thermal Conductivity

Global symmetric classical solutions for radiative compressible Navier‐Stokes equations with temperature‐dependent viscosity coefficients

Global symmetric solutions for a multi-dimensional compressible viscous gas with radiation in exterior domains

Contact Info

Product

Resources

About