Regularity criteria for the Euler equations with nondecaying data

The local-in-time existence and uniqueness of strong solutions to the Euler equations in the whole space with nondecaying and certainly regular initial velocity are concerned. It is obtained that the spatial regularity of solutions coincides with that of initial velocity under the suitable setting of external forcing terms. Regularity criteria focusing into the vorticity are also discussed due to the similar arguments of Beale–Kato–Majda.