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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Elementary proofs of local energy conservation are obtained for bounded weak Euler solutions with measure first derivatives or vorticity, avoiding convolution kernel choices by using the Euler nonlinearity.
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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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Fine dissipative properties of Euler solutions with measure first derivatives
Elementary proofs of local energy conservation are obtained for bounded weak Euler solutions with measure first derivatives or vorticity, avoiding convolution kernel choices by using the Euler nonlinearity.