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.
Delort,Existence de nappes de tourbillon en dimension deux, Journal of the American Mathematical Society4(1991), no
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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.