The magnetohydrodynamics system consists of the Navier-Stokes and Maxwell's equations, coupled through multiples nonlinear terms. Such a forced by space-time white noise has been studied physicists for decades, rigorous proof its solution theory recently established in Yamazaki (2019, arXiv:1910.04820 [math.AP]) using paracontrolled distributions technique renormalizations. When an equation is ...

Abstract The SWEAP instrument suite on Parker Solar Probe (PSP) has detected numerous proton beams associated with coherent, circularly polarized, ion-scale waves observed by PSP’s FIELDS suite. Measurements during PSP Encounters 4?8 revealed pronounced complex shapes in the velocity distribution functions (VDFs), which tip of beam undergoes strong perpendicular diffusion, resulting VDF level c...