Decay of solutions to a linear viscous asymptotic model for water waves

Olivier Goubet , Guillaume Warnault

Chinese Annals of Mathematics, Series B ›› 2010, Vol. 31 ›› Issue (6) : 841 -854.

PDF
Chinese Annals of Mathematics, Series B ›› 2010, Vol. 31 ›› Issue (6) : 841 -854. DOI: 10.1007/s11401-010-0615-2
Article

Decay of solutions to a linear viscous asymptotic model for water waves

Author information +
History +
PDF

Abstract

The authors discuss a linear viscous asymptotic model for water waves and the decay rate of solutions towards the equilibrium.

Keywords

Water waves / Viscous asymptotic models / Nonlocal operators / Long-time asymptotics

Cite this article

Download citation ▾
Olivier Goubet, Guillaume Warnault. Decay of solutions to a linear viscous asymptotic model for water waves. Chinese Annals of Mathematics, Series B, 2010, 31(6): 841-854 DOI:10.1007/s11401-010-0615-2

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Amick C. J., Bona J. L., Schonbek M. E.. Decay of solutions of some nonlinear wave equations. J. Diff. Eqs., 1989, 81: 1-49

[2]

Bona J. L., Chen M., Saut J.-C.. Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media, I, Derivation and the linear theory. J. Nonlinear Sci., 2002, 12: 283-318

[3]

Brandolese, L. and Schonbek, M., Large time decay and growth for solutions of a viscous boussinesq system, to appear. arXiv:1003.4921

[4]

Chen M., Dumont S., Dupaigne L. Decay of solutions to a water wave model with a nonlocal viscous dispersive term. Discrete Contin. Dyn. Syst., 2010, 27(4): 1473-1492

[5]

Chen M., Goubet O.. Long-time asymptotic behavior of two-dimensional dissipative Boussinesq systems. Discrete Contin. Dyn. Syst., Ser. S, 2009, 2(1): 37-53

[6]

Dutykh D.. Visco-potential free-surface flows and long wave modelling. European Journal of Mechanics B/Fluids, 2009, 28(3): 430-443

[7]

Dutykh D., Dias F.. Viscous potential free-surface flows in a fluid layer of finite depth. C. R. Math. Acad. Sci. Paris, 2007, 345: 113-118

[8]

Hayashi N., Kaikina E., Naumkin P., Shishmarev I.. Asymptotics for Dissipative Nonlinear Equations, 2006, Berlin, Heidelberg: Springer-Verlag

[9]

Kakutani T., Matsuuchi K.. Effect of viscosity of long gravity waves. J. Phys. Soc. Japan, 1975, 39: 237-246

[10]

Linares F., Ponce G.. Introduction to Nonlinear Dispersive Equations, 2009, New York: Springer-Verlag

[11]

Liu P., Orfila A.. Viscous effects on transient long-wave propagation. J. Fluid Mech., 2004, 520: 83-92

[12]

Vento, S., Asymptotic behavior for dissipative KdV equations, to appear.

AI Summary AI Mindmap
PDF

106

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/