AI 中文总结
本文研究二维空间中测度值初始涡度情形，在初始涡度为狄拉克质量的特殊情况时，证明了初始涡度的动力学发散会使玻尔兹曼方程的解在极小时空层内从预期流体动力学极限强烈发散。
AI 中文摘要
众所周知，当马赫数和克努森数趋于零时，不可压缩纳维 - 斯托克斯系统的解在各种情形（弱或强）下是玻尔兹曼方程解的极限。特别是光滑解的情况目前已相当清楚。近期工作旨在选择尽可能接近不可压缩纳维 - 斯托克斯系统适定性对应函数空间的初始数据。本文处理二维空间中测度值初始涡度的情况：在初始涡度为狄拉克质量的特殊情形下，已知纳维 - 斯托克斯系统的唯一解是热方程的解。我们证明这种初始涡度（稍微平滑化）的动力学发散导致玻尔兹曼方程的一个解在非常小的时间层内以强烈方式从预期流体动力学极限发散。
英文摘要
It is well-known that solutions to the incompressible Navier-Stokes system are limits in various contexts (weak or strong), of solutions to the Boltzmann equation, when the Mach and the Knudsen numbers go to zero. In particular the case of smooth solutions is by now rather well understood. Recent works have aimed at choosing initial data in function spaces as close as possible to those corresponding to well-posedness for the incompressible Navier-Stokes system. This paper tackles the case of measurevalued initial vorticity, in two space dimensions: in the special case when the initial vorticity is a Dirac mass, it is known that the unique solution to the Navier-Stokes system is the solution to the heat equation. We prove that the kinetic emanation of this initial vorticity (slightly smoothed out) leads to a solution of the Boltzmann equation which diverges in a strong way and in a very small time layer, from the expected hydrodynamic limit.
