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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The authors establish pathwise non-uniqueness for stochastic incompressible Euler equations with a passive tracer in dimensions d >= 2 by constructing infinitely many global weak solutions to equivalent random PDEs using the Baire category method, extending prior deterministic results to arbitrary 0
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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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Non-uniqueness for the stochastic incompressible Euler equations with a passive tracer
The authors establish pathwise non-uniqueness for stochastic incompressible Euler equations with a passive tracer in dimensions d >= 2 by constructing infinitely many global weak solutions to equivalent random PDEs using the Baire category method, extending prior deterministic results to arbitrary 0