Hardy spaces and the two-dimensional Euler equations with nonnegative vorticity

Evans, L. C.; Müller, S.

doi:10.1090/S0894-0347-1994-1220787-3

Hardy spaces and the two-dimensional Euler equations with nonnegative vorticity
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by L. C. Evans and S. Müller

J. Amer. Math. Soc. 7 (1994), 199-219

DOI: https://doi.org/10.1090/S0894-0347-1994-1220787-3

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Abstract:

We prove that certain quadratic expressions involving the gradient of a weakly superharmonic function in ${\mathbb {R}^2}$ belong to a local Hardy space. As an application we provide a new proof of J.-M. Delort’s convergence theorem for solutions of the two-dimensional Euler equations with vorticities of one sign.

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