Shock waves for the Burgers equation and curvatures of diffeomorphism groups

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dc.creatorKhesin, Boris
dc.creatorMisiolek, Gerard
dc.date2007-02-07
dc.date.accessioned2026-07-07T07:45:21Z
dc.date.available2026-07-07T07:45:21Z
dc.descriptionWe establish a simple relation between curvatures of the group of volume-preserving diffeomorphisms and the lifespan of potential solutions to the inviscid Burgers equation before the appearance of shocks. We show that shock formation corresponds to a focal point of the group of volume-preserving diffeomorphisms regarded as a submanifold of the full diffeomorphism group and, consequently, to a conjugate point along a geodesic in the Wasserstein space of densities. This establishes an intrinsic connection between ideal Euler hydrodynamics (via Arnold's approach), shock formation in the multidimensional Burgers equation and the Wasserstein geometry of the space of densities.
dc.description11 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0702196
dc.identifierhttp://arxiv.org/abs/math/0702196
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123505
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject58B25; 35Q35
dc.titleShock waves for the Burgers equation and curvatures of diffeomorphism groups
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