Global solutions of the random vortex filament equation
نویسندگان
چکیده
منابع مشابه
Global Solutions of the Random Vortex Filament Equation
In this article we prove the existence of a global solution for the random vortex filament equation. Our work gives a positive answer to a question left open in recent publications: Berselli and Gubinelli [5] showed the existence of global solution for a smooth initial condition while Bessaih, Gubinelli, Russo [6] proved the existence of a local solution for a general initial condition. In this...
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We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is “unpinched” to produce a new pair of branch points and therefore a solution of higher genus. We prove that every step in this process correspon...
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For the class of quasiperiodic solutions of the vortex filament equation, we study connections between the algebro-geometric data used for their explicit construction, and the geometry of the evolving curves. We give a complete description of genus one solutions, including geometrically interesting special cases such as Euler elastica, constant torsion curves, and self-intersecting filaments. W...
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Differential calculus on the space of asymptotically linear curves is developed. The calculus is applied to the vortex filament equation in its Hamiltonian description. The recursion operator generating the infinite sequence of commuting flows is shown to be hereditary. The system is shown to have a description with a Hamiltonian pair. Master symmetries are found and are applied to deriving an ...
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We study an evolution problem in the space of continuous loops in threedimensional Euclidean space modelled upon the dynamics of vortex lines in 3d incompressible and inviscid fluids. We establish existence of a local solution starting from Hölder regular loops with index greater than 1/3. When the Hölder regularity of the initial condition X is smaller or equal 1/2 we require X to be a rough p...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2013
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/26/9/2499