论文标题
通过对流的dyson等温仿射解决方案，通过对流进行热传输的可压缩欧拉方程的全球解决方案
Global solutions to the compressible Euler equations with heat transport by convection around Dyson's isothermal affine solutions
论文作者
论文摘要
通过戴森的等温仿射溶液的扰动，在整个空间中通过对流进行热传输的可压缩欧拉方程的全球解决方案被证明存在。由于密度无限行为的真空真空，这种设置带来了新的困难。特别是，等温运动的扰动将高斯功能引入我们的稳定性分析中，并且证明了新的有限传播结果可以处理由高斯的存在引起的潜在无界术语。但是，通过使用这种有限的传播结果来减轻背景运动的关键稳定效果，并使用新的时间重量操纵来仔细地使用热传输配方来建立全球存在。对流的热传输为模型提供了独特的物理见解，并从数学上讲，我们在对系统的这一特征的分析中使用受控的空间扰动，从而导致我们作为技术的一部分来利用源术语估计。
Global solutions to the compressible Euler equations with heat transport by convection in the whole space are shown to exist through perturbations of Dyson's isothermal affine solutions. This setting presents new difficulties because of the vacuum at infinity behavior of the density. In particular, the perturbation of isothermal motion introduces a Gaussian function into our stability analysis and a novel finite propagation result is proven to handle potentially unbounded terms arising from the presence of the Gaussian. Crucial stabilization-in-time effects of the background motion are mitigated through the use of this finite propagation result however and a careful use of the heat transport formulation in conjunction with new time weight manipulations are used to establish global existence. The heat transport by convection offers unique physical insights into the model and mathematically, we use a controlled spatial perturbation in the analysis of this feature of our system which leads us to exploit source term estimates as part of our techniques.
