Kazantsev-Kraichnan模型中的反常正则化
Anomalous Regularization in Kazantsev-Kraichnan Model
AI总结：
本文研究了在无散度高斯速度场输运和拉伸下的被动向量场，证明了尽管存在可能引发奇异性的拉伸项，正则化效应在$d\ge 3$维度的特定区间内仍得以保留，并应用于3D Euler方程和磁流体湍流感应方程。
摘要：
本文研究一个被动向量场，它由一个无散度的高斯速度场输运和拉伸，该速度场在时间上delta相关，在空间上弱相关（空间非光滑）。尽管标量场的输运（Kraichnan被动标量模型）已知具有正则化性质，但向量输运中潜在竞争的拉伸项可能引发奇异性形成。我们证明正则化效应在某些区间内实际得以保留。虽然这在任何维度$d\ge 3$下均成立，但它显著地暗示了带有湍流速度随机建模的线性化3D Euler方程以及磁流体动力学湍流中感应方程的正则化结果。
英文摘要：
This work investigates a passive vector field which is transported and stretched by a divergence-free Gaussian velocity field, delta-correlated in time and poorly correlated in space (spatially nonsmooth). Although the advection of a scalar field (Kraichnan's passive scalar model) is known to enjoy regularizing properties, the potentially competing stretching term in vector advection may induce singularity formation. We establish that the regularization effect is actually retained in certain regimes. While this is true in any dimension $d\ge 3$, it notably implies a regularization result for linearized 3D Euler equations with stochastic modeling of turbulent velocities, and for the induction equation in magnetohydrodynamic turbulence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
