On a stochastic Korteweg-de Vries equation with homogeneous noise

Anne de Bouard[1]; Arnaud Debussche[2]

  • [1] Centre de Mathématiques Appliquées, UMR 7641 CNRS/Ecole Polytechnique, 91128 Palaiseau cedex, France
  • [2] ENS de Cachan, Antenne de Bretagne, Av. R. Schumann, 35170 Bruz, France

Séminaire Équations aux dérivées partielles (2007-2008)

  • page 1-13

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de Bouard, Anne, and Debussche, Arnaud. "On a stochastic Korteweg-de Vries equation with homogeneous noise." Séminaire Équations aux dérivées partielles (2007-2008): 1-13. <http://eudml.org/doc/11181>.

@article{deBouard2007-2008,
affiliation = {Centre de Mathématiques Appliquées, UMR 7641 CNRS/Ecole Polytechnique, 91128 Palaiseau cedex, France; ENS de Cachan, Antenne de Bretagne, Av. R. Schumann, 35170 Bruz, France},
author = {de Bouard, Anne, Debussche, Arnaud},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {stochastic KdV equation; global existence and uniqueness; homogeneous noise},
language = {eng},
pages = {1-13},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {On a stochastic Korteweg-de Vries equation with homogeneous noise},
url = {http://eudml.org/doc/11181},
year = {2007-2008},
}

TY - JOUR
AU - de Bouard, Anne
AU - Debussche, Arnaud
TI - On a stochastic Korteweg-de Vries equation with homogeneous noise
JO - Séminaire Équations aux dérivées partielles
PY - 2007-2008
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 13
LA - eng
KW - stochastic KdV equation; global existence and uniqueness; homogeneous noise
UR - http://eudml.org/doc/11181
ER -

References

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  1. T. B. Benjamin, The stability of solitary waves, Proc. Roy. Soc. London A328 (1972), 153–183. MR338584
  2. A. de Bouard, W. Craig, O. Diaz-Espinosa, P. Guyenne and C. Sulem, Long wave expansions for water waves over random topography, preprint ArXiv : 0710.0389. Zbl1228.76029
  3. A. de Bouard and A. Debussche, Random modulation of solitons for the stochastic Korteweg-de Vries equation, Ann. Inst. H. Poincaré Anal. Non Linéaire24 (2007), 251–278. Zbl1158.60359MR2310695
  4. A. de Bouard and A. Debussche, The Korteweg-de Vries equation with multiplicative homogeneous noise, in “Stochastic Differential Equations : Theory and Applications”, P.H. Baxendale and S.V. Lototsky Ed., Interdisciplinary Math. Sciences vol. 2, World Scientific, 2007. Zbl1137.35086
  5. A. de Bouard, A. Debussche and Y. Tsutsumi, White noise driven Korteweg-de Vries equation, J. Funct. Anal.169 (1999), 532–558. Zbl0952.60062MR1730557
  6. A. de Bouard, A. Debussche and Y. Tsutsumi, Periodic solutions of the Korteweg-de Vries equation driven by white noise, SIAM J. Math. Anal.36 (2004/2005), 815–855. Zbl1075.35121MR2111917
  7. A. de Bouard, E. Gautier, Exit problems related to the persistence of solitons for the Korteweg-de Vries equation with small noise, preprint ArXiv : 0801.3894. Zbl1185.35246
  8. W. Craig, An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits, Comm. Partial Differential Equations8 (1985), 787–1003. Zbl0577.76030MR795808
  9. J. Garnier, Long time dynamics of Korteweg-de Vries solitons driven by random perturbations, J. stat. Phys.105 (2001), 789–833. Zbl0999.35086MR1869566
  10. J. Garnier, J.C. Muñoz Grajales and A. Nachbin, Effective behaviour of solitary waves over random topography, Multiscale Model. Simul.6 (2007), 995–1025. Zbl1151.76388MR2368977
  11. S. Kuksin and A. Piatnitski, Khasminskii-Whitham averaging for randomly perturbed KdV equation, J. Math. Pures Appl.89 (2008), 400–428. Zbl1148.35077MR2401144
  12. R.L. Pego and M.I. Weinstein, Asymptotic stability of solitary waves, Comm. Math. Phys.164 (1994), 305–349. Zbl0805.35117MR1289328
  13. J. Printems, Aspects Théoriques et numériques de l’équation de Korteweg-de Vries stochastique, thèse, Université Paris-Sud, Orsay, France, 1998. 
  14. R. Rosales and G. Papanicolaou, Gravity waves in a channel with a rough bottom, Stud. Appl. Math.68 (1983), 89–102. Zbl0516.76018MR693716
  15. M. Scalerandi, A. Romano and C.A. Condat, Korteweg-de Vries solitons under additive stochastic perturbations, Phys. Review E58 (1998), 4166–4173. 
  16. Y. Tsutsumi, Time decay of solution for the KdV equation with multiplicative space-time noise, preprint, 2007. 
  17. M. Wadati, Stochastic Korteweg-de Vries equations, J. Phys. Soc. Japan52 (1983), 2642–2648. MR722214

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