论文标题
关于三维，不可压缩的galerkin截断的Euler方程的热化
On the thermalization of the three-dimensional, incompressible, Galerkin-truncated Euler equation
论文作者
论文摘要
在这种有限维系统中，由于相位空间和动能保存，galerkin截断的三维欧拉方程的长期解决方案松弛至绝对平衡。这些热化溶液的特征是速度场的吉布斯分布和其（有限）傅立叶模式之间的动能均衡。现在，通过详细的数值模拟，我们显示了物理空间中不可避免的热化的触发器，以及该问题如何减少到有效的一维问题，从而使与研究较高的汉堡方程进行比较。我们还讨论了我们对热化机制的理解如何被利用，以获得数值的欧拉方程的耗散解决方案，以及计算机模拟中有限时间爆炸的证据。
The long-time solutions of the Galerkin-truncated three-dimensional, incompressible Euler equation relax to an absolute equilibrium as a consequence of phase space and kinetic energy conservation in such a finite-dimensional system. These thermalized solutions are characterised by a Gibbs distribution of the velocity field and kinetic energy equipartition amongst its (finite) Fourier modes. We now show, through detailed numerical simulations, the triggers for the inevitable thermalization in physical space and how the problem is reducible to an effective one-dimensional problem making comparisons with the more studied Burgers equation feasible. We also discuss how our understanding of the mechanism of thermalization can be exploited to numerically obtain dissipative solutions of the Euler equations and evidence for or against finite-time blow-up in computer simulations.
