无发散对称张量的射影性质和气体动力学中新的色散估计
Projective properties of Divergence-free symmetric tensors, and new dispersive estimates in gas dynamics
摘要：
无发散对称张量类在连续介质力学中是普遍存在的。我们证明了它在自变量的射影变换下的不变性。这个作用量保持了正性，推广了Sophus Lie对牛顿动力学的群分析，当应用于气体动力学模型--如Euler系统或Boltzmann方程--结合补偿可积性时，得到了新的色散估计。最准确的一个是单原子气体。那么$tρ^\frac1d p$的时空积分仅以总质量和转动惯量有界。
英文摘要：
The class of Divergence-free symmetric tensors is ubiquitous in Continuum Mechanics. We show its invariance under projective transformations of the independent variables. This action, which preserves the positiveness, extends Sophus Lie's group analysis of Newtonian dynamics.When applied to models of gas dynamics --~such as Euler system or Boltzmann equation,~-- in combination with Compensated Integrability, this yields new dispersive estimates. The most accurate one is obtained for mono-atomic gases. Then the space-time integral of $tρ^\frac1d p$ is bounded in terms of the total mass and moment of inertia alone.
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