BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sung-Jin Oh (University of California Berkeley) DTSTART:20200625T150000Z DTEND:20200625T155000Z DTSTAMP:20260423T021119Z UID:IMS/32 DESCRIPTION:Title: On the Cauchy problem for the Hall magnetohydrodynamics\nby Sung-Jin Oh ( University of California Berkeley) as part of PDE seminar via Zoom\n\n\nAb stract\nIn this talk\, I will describe a recent series of work with I.-J. Jeong on the Hall MHD equation without resistivity. This PDE\, first inves tigated by the applied mathematician M. J. Lighthill\, is a one-fluid desc ription of magnetized plasmas with a quadratic second-order correction ter m (Hall current term)\, which takes into account the motion of electrons r elative to positive ions. Curiously\, we demonstrate the ill(!)posedness o f the Cauchy problem near the trivial solution\, despite the apparent line ar stability and conservation of energy. On the other hand\, we identify s everal regimes in which the Cauchy problem is well-posed\, which not only includes the original setting that M. J. Lighthill investigated (namely\, for initial data close to a uniform magnetic field) but also possibly larg e perturbations thereof. Central to our proofs is the viewpoint that the H all current term imparts the magnetic field equation with a quasilinear di spersive character. With such a viewpoint\, the key ill- and well-posednes s mechanisms can be understood in terms of the properties of the bicharact eristic flow associated with the appropriate principal symbol.\n\nhttps:// nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n LOCATION:https://researchseminars.org/talk/IMS/32/ END:VEVENT END:VCALENDAR