Global existence for non-homogeneous incompressible inviscid fluids in the presence of Ekman pumping

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In this paper, we study the solvability of the density-dependent incompressible Euler equations, supplemented with a damping term of the form [Formula: see text], where [Formula: see text] and [Formula: see text]. In the general case of space dimension [Formula: see text], we establish global well-posedness in the Besov spaces framework, under a non-linear smallness condition involving the size of the initial velocity field [Formula: see text], of the initial non-homogeneity [Formula: see text] and of the damping coefficient [Formula: see text]. In the specific situation of planar motions and damping term with [Formula: see text], we exhibit a second smallness condition implying global existence, which in particular yields global well-posedness for arbitrarily large initial velocity fields, provided the initial density variations [Formula: see text] are small enough. The formulated smallness conditions rely only on the endpoint Besov norm [Formula: see text] of the initial datum, whereas, as a byproduct of our analysis, we derive exponential decay of the velocity field and of the pressure gradient in the high regularity norms [Formula: see text].