论文标题
具有粘度和热导率的辐射流体动力学模型的全球规律性
Global Regularity for A Radiation Hydrodynamics Model with Viscosity and Thermal Conductivity
论文作者
论文摘要
在本文中，我们研究了具有粘度和导热率的辐射流体动力学模型的全球良好性。现在，理解的是，与可压缩的欧拉方程式不同，它们的平滑解决方案必须在有限的时间内吹出，无论多么小，初始数据的平滑程度，这种辐射流体流体动力学模型的耗散结构可以确保其一维的cauchy问题确实可以保证其一维cauchy问题能够确保其最初的数据足以使访问量足够小，但即使是震惊的数据，即使是震惊的范围，因此，即使是震惊的范围，也可以将其引起范围，即使是震惊的效果，即使是震惊的范围，而且很小的数据是震惊的。必须在有限的时间内出现奇点，以使其具有导热率和零粘度的一维辐射流体动力学模型的库奇问题平滑解决方案。因此，一个自然的问题是，如果考虑粘度和热导率的影响，是否存在具有粘度和热导率的一维辐射流体动力学模型？我们对此问题给出了肯定的答案，并在本文中表明，在一维周期盒中，辐射流体动力学模型的初始有限值问题t = r/z具有粘度和热导率确实存在着一个独特的全局平滑解决方案，用于任何大型初始数据。我们的分析中的主要成分是引入一些微妙的估计值，尤其是对绝对温度的估计值和宏辐射通量的一阶空间衍生物之间的估计值，以推导所需的正度下限和上限的密度和绝对温度。
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 an 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 estimate on the absolute temperature 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.
