Journal of the
Korean Mathematical Society JKMS

In this paper, we disscuss a uniqueness problem for the Cauchy problem of the Euler equation. We give a sufficient condition on the vorticity to show the uniquness of a class of generalized solution in terms of the generalized Besov space. The condition allows the iterated logarithmic singularity to the vorticity of the solution. We also disscuss the break down (or blow up) condition for a smooth solution to the Euler equation under the related assumption.

Keywords: Euler equation, uniqueness, blow-up, weak solution, Besov space, vorticity

MSC numbers: Primary 35Q05, secondary 75C05, 35L60