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We show that for any $\al<\frac 17$ there exist $\al$-H\"older continuous weak solutions of the three-dimensional incompressible Euler equation, which satisfy the local energy inequality and strictly dissipate the total kinetic energy.
Statistical hydrodynamics
L. Onsager · 1949
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Partial regularity of suitable weak solutions of the Navier-Stokes equations
L. Caffarelli, R. Kohn, and L. Nirenberg · 1982
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Onsager’s conjecture on the energy conservation for solutions of Euler’s equation
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P. Isett and V. Vicol · 2015
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Regularity in time of Hölder solutions of Euler and hypodissipative Navier-Stokes equations
M. Colombo and L. De Rosa · 2020
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