Decay of solutions to a viscous asymptotical model for waterwaves : Kakutani – Matsuuchi model

@inproceedings{Chen2012DecayOS,
  title={Decay of solutions to a viscous asymptotical model for waterwaves : Kakutani – Matsuuchi model},
  author={Min Chen and S. Dumont and Olivier Goubet},
  year={2012}
}
In this article, we study a viscous asymptotical model equation for water waves ut + ux − βutxx + ν  D 1 2 u + F −1(i | ξ | 1 2 sgn(ξ)u(ξ))+ γ uux = 0 proposed in Kakutani and Matsuuchi (1975) [6]. Theoretical questions including the existence and regularity of the solutions will be answered. Numerical simulations of its solutions will be carried out and the effects of various parameters will be investigated. We will also predict the decay rate of its solutions towards the equilibrium… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 18 references

Effect of viscosity of long gravity waves

  • T. Kakutani, M. Matsuuchi
  • J. Phys. Soc. Japan 39
  • 1975
Highly Influential
15 Excerpts

Numerical investigation of a two-dimensional Boussinesq system

  • M. Chen
  • Discrete Contin. Dyn. Syst. 28 (4)
  • 2009
Highly Influential
5 Excerpts

Numerical study of the regularized long - wave equation 1 : numerical methods

  • G. R. McGuire J. C. Eylbeck
  • Dyn . Syst .
  • 2007

Asymptotics for Dissipative Nonlinear Equations

  • N. Hayashi, E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev
  • in: Lecture Notes in Mathematics, vol. , Springer…
  • 2006
1 Excerpt

Numerical investigation of a two - dimensional Boussinesq system , Discrete Contin

  • M. Chen
  • Asymptotics for Dissipative Nonlinear Equations…
  • 2006

Viscous effects on transient long wave propagation

  • P. Liu, A. Orfilla
  • J. Fluid Mech. 520
  • 2004
1 Excerpt