发表机构
Dalian University of Technology; Shenzhen University; University of Wisconsin–Madison（大连理工大学; 深圳大学; 威斯康星大学麦迪逊分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究建立了粗糙轴对称欧拉流的全局能量紧性，并利用它构造了碰撞动力学方程的流体动力学极限，实现了跨越欧拉正则性破缺的能量守恒延拓。
AI 中文摘要
我们建立了无旋三维轴对称欧拉流的全局能量紧性，并利用它构造了在有限时间欧拉正则性破缺之后的碰撞动力学方程的流体动力学极限。对于相对涡量属于$L^1\cap L^p$的情形，当$p\ge4/3$时，正则近似欧拉流在$C_tL_x^2$中全局紧，且无需符号条件或任何空间矩假设。当$p<4/3$时，在绝对冲量的均匀控制下，同样的结论成立。我们确定了控制这种约束的尖锐径向动力学：当$p\ge5/3$时，绝对冲量在无符号条件下传播；而当$1<p<5/3$时，绝对冲量在单侧$L^{p^\sharp}$可积性下受控，其中$p^\sharp=4p/(3p-1)$，且该指数是尖锐的。特别地，对于单符号有限冲量涡量，所得的全局能量紧性在整个范围$p>1$内成立。对于库仑朗道方程和一类非截断软势玻尔兹曼方程，我们在寿命$T^\varepsilon\to\infty$上构造了强解，实现了规定的粗糙有限能量欧拉初值，并在每个固定时间区间上获得了能量守恒的轴对称欧拉极限。如果相应的正则欧拉演化在有限时间内失去正则性，则流体动力学场在奇异时间之前收敛到正则欧拉解，并在该处具有共同的强迹，而子序列产生全局能量守恒的欧拉延拓，越过该时间。
英文摘要
We establish global energy compactness for rough three-dimensional axisymmetric Euler flow without swirl and use it to construct hydrodynamic limits of collisional kinetic equations beyond finite-time Euler regularity breakdown. For relative vorticity in $L^1\cap L^p$, regular approximate Euler flows are globally compact in $C_tL_x^2$ for $p\ge4/3$, without a sign condition or any spatial-moment assumption. Below $4/3$, the same conclusion holds under uniform control of the absolute impulse. We identify the sharp radial dynamics governing this confinement: the absolute impulse is propagated without a sign condition for $p\ge5/3$, while for $1<p<5/3$ it is controlled under one-sided $L^{p^\sharp}$ integrability, where $p^\sharp= {4p} / (3p-1)$, and this exponent is sharp. In particular, for one-sign finite-impulse vorticity the resulting global energy compactness holds throughout the full range $p>1$. For the Coulomb Landau equation and a class of non-cutoff soft-potential Boltzmann equations, we construct strong solutions on lifespans $T^\varepsilon\to\infty$ realizing prescribed rough finite-energy Euler initial data and obtain energy-conserving axisymmetric Euler limits on every fixed time interval. If the corresponding regular Euler evolution loses regularity in finite time, the hydrodynamic fields converge to the regular Euler solution up to the singular time and have a common strong trace there, while subsequences yield global energy-conserving Euler continuations past that time.
Comments107 pages. All comments are welcome
