Unique local existence of solution in low regularity space of the Cauchy problem for the mKdV equation with periodic boundary condition

Kenji Nakanishi[1]; Hideo Takaoka[2]; Yoshio Tsutsumi[1]

  • [1] Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
  • [2] Department of Mathematics, Faculty of Science, Kobe University, Kobe 657-8501, Japan

Séminaire Équations aux dérivées partielles (2007-2008)

  • Volume: 2007-2008, page 1-5

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Nakanishi, Kenji, Takaoka, Hideo, and Tsutsumi, Yoshio. "Unique local existence of solution in low regularity space of the Cauchy problem for the mKdV equation with periodic boundary condition." Séminaire Équations aux dérivées partielles 2007-2008 (2007-2008): 1-5. <http://eudml.org/doc/11173>.

@article{Nakanishi2007-2008,
affiliation = {Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan; Department of Mathematics, Faculty of Science, Kobe University, Kobe 657-8501, Japan; Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan},
author = {Nakanishi, Kenji, Takaoka, Hideo, Tsutsumi, Yoshio},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {modified Korteweg-de Vries equation; one-dimensional torus; Cauchy problem},
language = {eng},
pages = {1-5},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Unique local existence of solution in low regularity space of the Cauchy problem for the mKdV equation with periodic boundary condition},
url = {http://eudml.org/doc/11173},
volume = {2007-2008},
year = {2007-2008},
}

TY - JOUR
AU - Nakanishi, Kenji
AU - Takaoka, Hideo
AU - Tsutsumi, Yoshio
TI - Unique local existence of solution in low regularity space of the Cauchy problem for the mKdV equation with periodic boundary condition
JO - Séminaire Équations aux dérivées partielles
PY - 2007-2008
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2007-2008
SP - 1
EP - 5
LA - eng
KW - modified Korteweg-de Vries equation; one-dimensional torus; Cauchy problem
UR - http://eudml.org/doc/11173
ER -

References

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  9. —, On the ill-posedness of some canonical dispersive equations, Duke Math. J. 106 (2001), 617–633. Zbl1034.35145MR1813239
  10. S. Klainerman and M. Machedon, Space time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math. 46 (1993), 1221–1268. Zbl0803.35095MR1231427
  11. H. Koch and N. Tzvetkov, Nonlinear wave interactions for the Benjamin-Ono equation, Int. Math. Res. Not. 30 (2005), 1833–1847. Zbl1156.35460MR2172940
  12. H. Takaoka and Y. Tsutsumi, Well-posedness of the Cauchy problem for the modified KdV equation with periodic boundary condition, Internat. Math. Res. Notices 56 (2004), 3009–3040. Zbl1154.35442MR2097834
  13. T. Tao, Global well-posedness of the Benjamin-Ono equation in H 1 ( ℝ ) , J. Hyperbolic Differ. Equ. 1 (2004), 27–49. Zbl1055.35104MR2052470

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