Summary: We present the conditions of existence and uniqueness for the solutions of nonlinear partial differential equations that describe the average horizontal streams in a sea, under wind influence. In a previous note [P. Orenga, Analyse de quelques problèmes en océanographie physique. Univ. de Corse (1989)] we treated this problem with the usual hypothesis that friction on the bottom and shore is negligible compared to the energy dissipation of the fluid; we pointed then out the difficulty generated by the multiconnexity of the domain in this scheme of hypothesis: these special boundary conditions lead to existence of nondissipative functions with \(\Delta u=0\). We show that keeping the terms of friction on the bottom or on the shore permits to remove this difficulty.