Asymptotic properties of deep water solitary waves with compactly supported vorticity
In this thesis, we consider two- and three-dimensional gravity and capillary-gravity solitary waves propagating along the surface of a body of water with infinite depth.The waves are acted upon by gravity and we allow the effect of surface tension but do not require it. In addition, we assume that the flow is only rotational on some compact set inscribed in the domain of the fluid. Under some decay assumptions, we show that the velocity potential behaves like a dipole at in nity and obtain asymptotics form of the velocity potential and thefree surface. We manage to rule out waves of pure elevation and depression. We also exhibit an equation relating the total momentum in the Cauchy principal valuesense with the dipole moment. This equation combined with the theorem on angularmomentum tells us that nite angular momentum implies zero total momentum in theCauchy principal value sense. Moreover, if the horizontal component of the velocity eld of a wave is non-zero, then such wave has an in nite angular momentum.