Symmetry of free-surface flows (Q1188032)

The 2-D (mainly supercritical) flows considered are essentially (i) solitary waves in immiscible fluids of different density and (ii) steady waves in a free surface of a fluid flowing past an object (such as a ship hull, a hydrofoil or surfboard). The results include statements of positivity, monotonicity, symmetry and the asymptotic behavior at infinity. For (i) several results on the exponential decay of the solutions are given; the reviewer senses some connection here to the results of \textit{L. V. Ovsyannikov} [Sov. Phys., Dokl. 36, No. 5, 365-367 (1991); translation from Dokl. Akad. Nauk SSSR 318, No. 3, 556-559 (1991)]. For (ii) it is shown that if the wetted surface of the obstacle is completely above the undisturbed free surface, the wave levation cannot be negative anywhere.