Rough transport noise selects the unique DiPerna-Lions solution in the zero-noise limit and yields a large deviations principle in the non-separable space L^∞_t L^p_x.
Anomalous Regularization in Kazantsev-Kraichnan Model
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abstract
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.
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Zero-noise selection and Large Deviations in $L^\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions
Rough transport noise selects the unique DiPerna-Lions solution in the zero-noise limit and yields a large deviations principle in the non-separable space L^∞_t L^p_x.