高维粘性辐射反应流体力学方程组的大初值整体强解

The equations of radiative and reactive flows can describe the dynamic combustion phenomenon of reacting fluids with viscosity and heat-conductivity. The mathematical theory on multi-dimensional global solutions to these equations with large initial data has become a research focus in the field of partial differential equations. But the currently available results are only restricted to the symmetric case with constant viscosity coefficients. According to physical experimental results and the kinetic theory, the viscosity coefficients depend on the temperature. In this project, we will study the existence and uniqueness of global strong solutions to radiative and reactive flows in the two-dimensional case and the symmetric case with temperature-dependent viscosity coefficients.

辐射反应流体力学方程组可以用来描述具有粘性及热传导的反应流体的动态燃烧现象。关于其高维大初值整体强解的数学理论已成为偏微分方程领域所关注的焦点之一。但目前相关的结果仅限于粘性系数为常数的对称情形。由物理实验结果以及动理学理论可知，粘性系数是依赖于温度的。本项目拟研究辐射反应流体在二维情形以及粘性系数依赖于温度时的对称情形下的大初值整体强解的存在性和唯一性。

本项目主要研究来源于流体动力学的两类非线性偏微分方程定解问题的整体适定性及大时间渐近行为。在本项目的资助下，我们证明了外区域中可压缩粘性辐射流体的高维对称解的存在性及其渐近稳定性，以及一维和二维情形下可压缩微极流体力学方程组全局解的存在性及其大时间行为。