, Volume 214, Issue 1, pp 191-200

Limiting Case of the Sobolev Inequality in BMO,¶with Application to the Euler Equations

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We shall prove a logarithmic Sobolev inequality by means of the BMO-norm in the critical exponents. As an application, we shall establish a blow-up criterion of solutions to the Euler equations.

Received: 2 March 1999 / Accepted: 29 March 2000