PDE Real Analysis Seminar
Seminar information archive ~02/12|Next seminar|Future seminars 02/13~
Date, time & place | Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
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Organizer(s) | Yoshikazu Giga, Kazuhiro Ishige, Hiroyoshi Mitake, Tsuyoshi Yoneda |
URL | https://www.math.sci.hokudai.ac.jp/coe/sympo/pde_ra/index_en.html |
2016/03/16
16:00-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Boris Khesin (University of Toronto)
Fluids, vortex membranes, and skew-mean-curvature flows (English)
Boris Khesin (University of Toronto)
Fluids, vortex membranes, and skew-mean-curvature flows (English)
[ Abstract ]
We show that an approximation of the hydrodynamical Euler equation describes the skew-mean-curvature flow on vortex membranes in any dimension. This generalizes the classical binormal, or vortex filament, equation in 3D. We present a Hamiltonian framework for dynamics of higher-dimensional vortex filaments and vortex sheets as singular 2-forms (Green currents) with support of codimensions 2 and 1, respectively.
We show that an approximation of the hydrodynamical Euler equation describes the skew-mean-curvature flow on vortex membranes in any dimension. This generalizes the classical binormal, or vortex filament, equation in 3D. We present a Hamiltonian framework for dynamics of higher-dimensional vortex filaments and vortex sheets as singular 2-forms (Green currents) with support of codimensions 2 and 1, respectively.