BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Valentin Lychagin DTSTART:20250312T162000Z DTEND:20250312T180000Z DTSTAMP:20260423T024832Z UID:GDEq/128 DESCRIPTION:Title: T urbulence geometry and Navier-Stokes equations\nby Valentin Lychagin a s part of Geometry of differential equations seminar\n\nLecture held in ro om 303 of the Independent University of Moscow.\n\nAbstract\nIt is propose d to consider turbulent media and\, in particular\, random vector fields f rom a geometric point of view. This leads to a geometry similar to\, but n ot identical to\, Finsler's.\n\nWe show that a turbulence generates a hori zontal differential symmetric 2-form on the tangent bundle\, which we call the Mahalanobis metric.\n\nThus\, vector fields on the underlying manifol d generate Riemannian structures on it by the restriction of the Mahalanob is metric on the graphs of vector fields.\n\nIn the case of so-called Gaus sian turbulences\, these Riemannian structures coincide and generate a uni que Riemannian structure.\n\nMoreover\, similar to Finsler geometry\, turb ulence generates a nonlinear connection in the tangent bundle but the Maha lanobis metric generates an affine connection in the tangent bundle.\n\nTh is affine connection and the Mahalanobis metric give us everything we need to construct the Navier-Stokes equations for turbulent media.\n\nWe will present two implementations of this scheme: for the flow of ideal gases an d plasma\, where turbulence is described by the Maxwell-Boltzmann distribu tion law\, and compare them with the standard Navier-Stokes equations.\n LOCATION:https://researchseminars.org/talk/GDEq/128/ END:VEVENT END:VCALENDAR