Binormal flow
WebMay 1, 2009 · Abstract: In this paper we study the stability of the self-similar solutions of the binormal flow, which is a model for the dynamics of vortex filaments in fluids and super-fluids. These particular solutions $\chi_a(t,x)$ form a family of evolving regular curves of $\mathbb R^3$ that develop a singularity in finite time, indexed by a parameter ... 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 …
Binormal flow
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WebJul 20, 2024 · Abstract: 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 … WebSep 21, 2024 · In this talk I shall present a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear …
WebWe study curve motion by the binormal flow with curvature and torsion depending velocity and sweeping out immersed surfaces. Using the Gauss-Codazzi equations, we obtain … 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 ...
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 ... http://www.bcamath.org/documentos_public/archivos/publicaciones/1_The_Initial_Value_Problem_for_the_Binormal_Flow.pdf
WebJul 14, 2024 · We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object has a non-obvious nonlinear geometric interpretation. We recall that the binormal flow is a standard model …
WebApr 17, 2024 · The skew-mean-curvature (or binormal) flow in $${\mathbb {R}}^n,\;n\geqslant 3$$ with certain symmetry can be regarded as point vortex motion of these 2D lake equations. We compare point vortex motions of the Euler and lake equations. Interesting similarities between the point vortex motion in the half-plane, … refining of petroleum processWebMay 5, 2024 · See and its references for results on the flow . The existence of true solutions of that satisfy near a given curve \(\Gamma (\tau )\) that evolves by the binormal flow is an outstanding open question sometimes called the vortex filament conjecture. See and . This statement is unknown except for very special cases. refining of oilWebMar 11, 2024 · The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. This flow is also related to the classical continuous … refining of snWebThe 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, and the 1-D cubic Schrödinger equation. We consider a class of solutions at the critical level of regularity that generate singularities in finite ... refining oil industry jobsThe 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 refining of your faithWebWe study curve motion by the binormal flow with curvature and torsion depending velocity and sweeping out immersed surfaces. Using the Gauss-Codazzi equations, we obtain filaments evolving with constant torsion which arise from extremal curves of curvature energy functionals. They are “soliton” solutions in the sense that they … refining of used lube oilWebBinormal definition, the normal to a curve, lying perpendicular to the osculating plane at a given point on the curve. See more. refining of petroleum images