Global existence and decay rates of solutions to the viscous water-waves system. (English) Zbl 1496.35276
Summary: In this paper, we analyze a nonlinear model of the viscous water-waves equation proposed in [F. Dias et al., Phys. Lett., A 372, No. 8, 1297–1302 (2008; Zbl 1217.76018)]. To this end, we first study the linear model in [loc. cit.]. We then derive a new model which approximates the nonlinear model in [loc. cit.]. We finally show the existence of a unique global-in-time solution and its decay rates to this new system with small initial data in energy spaces.
MSC:
| 35Q30 | Navier-Stokes equations |
| 35Q35 | PDEs in connection with fluid mechanics |
| 76D27 | Other free boundary flows; Hele-Shaw flows |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
Keywords:
Dias-Dyachenko-Zakharov model; viscous water-waves; global well-posedness; temporal decay ratesCitations:
Zbl 1217.76018References:
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