WebMay 25, 2024 · Finally we prove the existence of a unique solution of the binormal flow with datum a polygonal line. This equation is used as a model for the vortex filaments … WebThe local induction equation, or the binormal flow on space curves is a well-known model of deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature is governed by the non-linear Schrödinger equation. In this article, we present its discrete analogue, namely, a model of deformation of discrete ...
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The vortex filaments are present in 3-D fluids having vorticity concentrated along a curve, and are a key element of quantum and classical fluid turbulent dynamics. This low regularity framework is difficult to analyze through the Euler and Navier–Stokes equation; it is however at the heart of current investigations (see … See more A classical problem of mathematical analysis is finding real variable functions that are continuous but not differentiable at any point. Although it … See more Let n\in {\mathbb {N}}^*, \nu \in ]0,1], \Gamma >0. Let \chi _n(0) be a polygonal line with corners located at j\in {\mathbb {Z}} with j \le n^\nu , of same torsion \omega _0 and angles \theta _nsuch that located and oriented … See more Our main statement asserts the existence of various families of solutions \{\chi _n\}_{n\in {\mathbb {N}}} of the binormal flow such that the … See more WebApr 3, 2013 · The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisenberg model in ferromagnetism ... easter speeches for a eleven year old boys
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Web[9] to deduce weak-strong uniqueness of solutions to binormal curvature flow. In the forthcoming work [7], we employ an energy-based strategy to deduce a weak-strong uniqueness theorem for multiphase mean curvature flow. 2. Definition of the relative entropy and Gronwall estimate. 2.1. Extending the unit normal vector field of the surface ... WebMay 25, 2024 · The binormal (curvature) flow, that we refer hereafter as BF, is the classical model for one vortex filament dynamics. It was derived by Da Rios 1906 in his PhD … WebSep 26, 2011 · We consider the binormal flow equation, which is a model for the dynamics of vortex filaments in Euler equations. Geometrically it is a flow of curves in three dimensions, explicitly connected to ... easter speech for kids