On strong convergence to 3D steady vortex sheets
نویسندگان
چکیده
منابع مشابه
Symplectic structure on vortex sheets
We present a Lie algebraic framework for vortex sheets as singular 2-forms with support of codimension 1, i.e. singular elements of a completion of the dual to the Lie algebra of divergence-free vector fields. This framework allows one to define the Poisson and symplectic structures on the space of vortex sheets, which interpolate between the corresponding structures on filaments and smooth vor...
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Standard numerical methods for the Birkhoff-Rott equation for a vortex sheet are unstable due to the amplification of roundoff error by the Kelvin-Helmholtz instability. A nonlinear filtering method was used by Krasny to eliminate this spurious growth of round-off error and accurately compute the Birkhoff-Rott solution essentially up to the time it becomes singular. In this paper convergence is...
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The motion of vortex sheets with surface tension has been analyzed in the setting of irrotational flows by Ambrose [1] and Ambrose & Masmoudi [2] in 2D, and by Ambrose & Masmoudi [3] in 3D. With irrotationality, the nonlinear Euler equations reduce to Poisson’s equation for the pressure function in the bulk, and the motion of the vortex sheet is decoupled from that of the fluid, thus allowing b...
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In 1966 V.Arnold suggested a group-theoretic approach to ideal hydrodynamics in which the motion of an inviscid incompressible fluid is described as the geodesic flow of the right-invariant L-metric on the group of volume-preserving diffeomorphisms of the flow domain. Here we propose geodesic, group-theoretic, and Hamiltonian frameworks to include fluid flows with vortex sheets. It turns out th...
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We are concerned with the stability of compressible vortex sheets in two-dimensional steady supersonic Euler flows over Lipschitz walls under a BV boundary perturbation, since steady supersonic Euler flows are important in many physical situations. It is proved that steady compressible vortex sheets in supersonic flow are stable in structure globally, even under the BV perturbation of the Lipsc...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2007
ISSN: 0022-0396
DOI: 10.1016/j.jde.2007.05.008