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 residual set of L² divergence-free initial data exists for which the 2D Euler equations admit unique global weak solutions that conserve energy and are recovered from Navier-Stokes vanishing-viscosity limits.
Dissipation in 2D inviscid fluid limits is Lebesgue in time and absolutely continuous w.r.t. defect measures, resulting in trivial or atomic measures under sign or oscillation conditions on initial vorticity.
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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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The 2D Euler equations are well-posed for generic initial data in $L^2$
A residual set of L² divergence-free initial data exists for which the 2D Euler equations admit unique global weak solutions that conserve energy and are recovered from Navier-Stokes vanishing-viscosity limits.
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Dissipation concentration in two-dimensional fluids
Dissipation in 2D inviscid fluid limits is Lebesgue in time and absolutely continuous w.r.t. defect measures, resulting in trivial or atomic measures under sign or oscillation conditions on initial vorticity.