BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jiao He (University of Evry - Paris Saclay) DTSTART:20200709T150000Z DTEND:20200709T155000Z DTSTAMP:20260423T010235Z UID:anpdews/27 DESCRIPTION:Title: Regularity criteria for weak solutions to the three-dimensional MHD syste m\nby Jiao He (University of Evry - Paris Saclay) as part of HA-GMT-PD E Seminar\n\n\nAbstract\nIn this talk we will first review various known r egularity criteria and partial regularity theory for 3D incompressible Nav ier-Stokes equations.\n\nI will then present two generalizations of partia l regularity theory of Caffarelli\, Kohn and Nirenberg to the weak solutio ns of MHD equations. The first one is based on the framework of parabolic Morrey spaces. We will show parabolic Hölder regularity for the "suitable weak solutions" to the MHD system in small neighborhoods. This type of pa rabolic generalization using Morrey spaces appears to be crucial when stud ying the role of the pressure in the regularity theory and makes it possib le to weaken the hypotheses on the pressure.\n\nThe second one is a regula rity result relying on the notion of "dissipative solutions". By making us e of the first result\, we will show the regularity of the dissipative sol utions to the MHD system with a weaker hypothesis on the pressure ($P \\in \\mathcal{D}'$).\n\nThis is a joint work with Diego Chamorro.\n LOCATION:https://researchseminars.org/talk/anpdews/27/ END:VEVENT END:VCALENDAR