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We study an initial value problem for the two-dimensional Euler equation. In particular, we consider the case where initial data belongs to a critical or subcritical Besov space, and initial vorticity is continuous with compact support. Under these assumptions, we conclude that the solution to the Euler equation loses an arbitrarily small amount of regularity as time evolves.

An Initial Value Problem for Two-Dimensional Ideal Incompressible Fluids With Continuous Vorticity