On the well-posedness of the incompressible density-dependent Euler equations in the Lp framework

The present paper is devoted to the study of the well-posedness issue for the density-dependent Euler equations in the whole space. We establish local-in-time results for the Cauchy problem pertaining to data in the Besov spaces embedded in the set of Lipschitz functions, including the borderline case Bp,1Np+1(RN). A continuation criterion in the spirit of the celebrated one by Beale, Kato and Majda (1984) in [2] for the classical Euler equations, is also proved.