Local existence and blow‐up criterion for the Euler equations in the Besov spaces

Article type: Research Article

Authors: Chae, Dongho

Affiliations: Department of Mathematics, Seoul National University, Seoul 151‐742, Korea E‐mail: [email protected]

Abstract: We prove the local in time existence and a blow‐up criterion of solutions in the Besov spaces for the Euler equations of inviscid incompressible fluid flows in Rn, n≥2. As a corollary we obtain the persistence of Besov space regularity for the solutions of the 2‐D Euler equations with initial velocity belonging to the Besov spaces. For the proof of the results we establish a logarithmic inequality of the Beale–Kato–Majda type and a Moser type of inequality in the Besov spaces.

Journal: Asymptotic Analysis, vol. 38, no. 3-4, pp. 339-358, 2004