BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Chanwoo Kim (University of Wisconsin-Madison) DTSTART:20200820T140000Z DTEND:20200820T145000Z DTSTAMP:20260423T035536Z UID:IMS/49 DESCRIPTION:Title: Inc ompressible Euler limit from Boltzmann equation with Boundary\nby Chan woo Kim (University of Wisconsin-Madison) as part of PDE seminar via Zoom\ n\n\nAbstract\nA rigorous derivation of the incompressible Euler equations with the no-penetration boundary condition from the Boltzmann equation wi th the diffuse reflection boundary condition has been a challenging open p roblem. We settle this open question in the affirmative when the initial d ata of fluid are well-prepared in a real analytic space\, in 3D half space . As a key of this advance we capture the Navier-Stokes equations satisfyi ng the no-slip boundary condition\, as an intermediary approximation of th e Euler equations through a new Hilbert-type expansion of the Boltzmann eq uation with the diffuse reflection boundary condition. Aiming to justify t he approximation we establish a novel quantitative $L^p-L^\\infty$ estimat e of the Boltzmann perturbation around a local Maxwellian of such viscous approximation\, along with the commutator estimates and the integrability gain of the hydrodynamic part in various spaces\; we also establish direct estimates of the Navier-Stokes equations in higher regularity with the ai d of the initial- boundary and boundary layer weights using a recent Green ’s function approach. The incompressible Euler limit follows as a byprod uct of our framework.\n\nhttps://nguyenquochung1241.wixsite.com/qhung/post /pde-seminar-via-zoom\n LOCATION:https://researchseminars.org/talk/IMS/49/ END:VEVENT END:VCALENDAR