论文标题
用于热传导流体的退化扩散系统的存在分析
Existence analysis of a degenerate diffusion system for heat-conducting fluids
论文作者
论文摘要
证明了抛物线能量传输系统的全球弱解决方案在具有无通量边界条件的有限域中的存在。该模型可以通过涉及非等温麦克斯韦式的线性碰撞算子从动力学方程中得出扩散极限。局部温度的演变受热方程式的控制，其源项取决于分布函数的能量。极限模型由具有熵结构的交叉扩散方程组成。主要困难是非标准退化，即，当流体密度或温度消失时，椭圆度就会丢失。存在证明是基于来自熵不等式的先验估计，$ h^{ - 1} $方法以及来自数学流体动力学的技术（重新归一化的配方，div-curl引理）。
The existence of global weak solutions to a parabolic energy-transport system in a bounded domain with no-flux boundary conditions is proved. The model can be derived in the diffusion limit from a kinetic equation with a linear collision operator involving a non-isothermal Maxwellian. The evolution of the local temperature is governed by a heat equation with a source term that depends on the energy of the distribution function. The limiting model consists of cross-diffusion equations with an entropy structure. The main difficulty is the nonstandard degeneracy, i.e., ellipticity is lost when the fluid density or temperature vanishes. The existence proof is based on a priori estimates coming from the entropy inequality and the $H^{-1}$ method and on techniques from mathematical fluid dynamics (renormalized formulation, div-curl lemma).
