Constructs divergence-free velocity fields and magnetic fields solving the kinematic dynamo equation on arbitrary smooth bounded domains in R^3 with arbitrarily fast magnetic energy growth uniformly as diffusivity vanishes, using convex integration with explicit potentials, and unifies the approach,
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A simpler proof of Vishik's nonuniqueness theorem for the forced 2D Euler equation is obtained by constructing an unstable vortex first as piecewise constant and then regularizing it via a fixed-point argument.
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Turbulent Dynamos on Bounded Domains and Their Generalization to the Geometric Transport Equation
Constructs divergence-free velocity fields and magnetic fields solving the kinematic dynamo equation on arbitrary smooth bounded domains in R^3 with arbitrarily fast magnetic energy growth uniformly as diffusivity vanishes, using convex integration with explicit potentials, and unifies the approach,
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A proof of Vishik's nonuniqueness Theorem for the forced 2D Euler equation
A simpler proof of Vishik's nonuniqueness theorem for the forced 2D Euler equation is obtained by constructing an unstable vortex first as piecewise constant and then regularizing it via a fixed-point argument.