Models for damped water waves

In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative effects and are obtained from the free boundary problems formulated in the works of Dias, Dyachenko and Zakharov (Physics Letters A, 2008), Jiang, Ting, Perlin and Schultz (Journal of Fluid Mechanics,1996) and Wu, Liu and Yue (Journal of Fluid Mechanics, 2006).