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Nonnegative measures belonging to \(H^{-1}(\mathbb{R}^2)\). (Les mesures positives appartenantes à \(H^{-1}(\mathbb{R}^2)\).) (English. French summary) Zbl 1323.35139

In this note, motivated by the 2D incompressible Euler system, the author shows that a non negative compactly supported Radon measure \(\mu\) belongs to \(H^{-1}(\mathbb R^2)\) provided that the function \(r\rightarrow \mu(B(0,r)\) is Hölder continuous.

MSC:

35Q31 Euler equations
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