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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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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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.
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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.