Strong compactness in the lowest norm making the nonlinearity well-defined prevents anomalous Hamiltonian dissipation for the generalized SQG equation in the inviscid limit, yielding global conservative weak solutions for critical initial data.
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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.
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Hamiltonian compactness and dissipation for the generalized SQG equation in the inviscid limit
Strong compactness in the lowest norm making the nonlinearity well-defined prevents anomalous Hamiltonian dissipation for the generalized SQG equation in the inviscid limit, yielding global conservative weak solutions for critical initial data.
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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.