Models for damped water waves. (English) Zbl 1431.35126
Summary: 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 F. Dias et al. [Phys. Lett., A 372, No. 8, 1297–1302 (2008; Zbl 1217.76018)], L. Jiang et al. [J. Fluid Mech. 329, 275–307 (1996; Zbl 0900.76014)], and G. Wu et al. [J. Fluid Mech. 556, 45–54 (2006; Zbl 1147.76031)].
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35R35 | Free boundary problems for PDEs |
| 35Q31 | Euler equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 76D33 | Waves for incompressible viscous fluids |
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