On the local and global well-posedness theory for the KP-I equation
Annales de l'I.H.P. Analyse non linéaire (2004)
- Volume: 21, Issue: 6, page 827-838
- ISSN: 0294-1449
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topKenig, Carlos E.. "On the local and global well-posedness theory for the KP-I equation." Annales de l'I.H.P. Analyse non linéaire 21.6 (2004): 827-838. <http://eudml.org/doc/78641>.
@article{Kenig2004,
author = {Kenig, Carlos E.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {capillary-gravity waves; surface tension; local well-posedness; global well-posedness},
language = {eng},
number = {6},
pages = {827-838},
publisher = {Elsevier},
title = {On the local and global well-posedness theory for the KP-I equation},
url = {http://eudml.org/doc/78641},
volume = {21},
year = {2004},
}
TY - JOUR
AU - Kenig, Carlos E.
TI - On the local and global well-posedness theory for the KP-I equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2004
PB - Elsevier
VL - 21
IS - 6
SP - 827
EP - 838
LA - eng
KW - capillary-gravity waves; surface tension; local well-posedness; global well-posedness
UR - http://eudml.org/doc/78641
ER -
References
top- [1] Bona J.L., Smith R., The initial value problem for the Korteweg–de Vries equation, Philos. Trans. Roy. Soc. London Ser. A278 (1975) 555-601. Zbl0306.35027MR385355
- [2] Bourgain J., On the Cauchy problem for the Kadomstev–Petviashvili equation, Geom. Funct. Anal.3 (1993) 315-341. Zbl0787.35086MR1223434
- [3] Coifman R., Meyer Y., Au delà des operateurs pseudodifferéntiels, Astérisque57 (1978). Zbl0483.35082MR518170
- [4] Colliander J., Kenig C., Staffilani G., Small solutions for the Kadomstev–Petviashvili I equation, Mosc. Math. J.1 (4) (2001) 491-520. Zbl1002.35108MR1901072
- [5] J. Colliander, C. Kenig, G. Staffilani, Low regularity solutions for the Kadomstev–Petviashvili I equation, Geom. Funct. Anal., submitted for publication. Zbl1039.35097MR2006556
- [6] J. Colliander, C. Kenig, G. Staffilani, Corrections to: On solutions for the Kadomstev–Petviashvili I equation, Mosc. Math. J., submitted for publication. Zbl1002.35108MR1901072
- [7] Iorio R.J., Nunes W.V.L., On equations of KP-type, Proc. Roy. Soc. Edinburgh Sect. A128 (1998) 725-743. Zbl0911.35103MR1635416
- [8] Journé J.L., Two problems of Calderón–Zygmund theory on product-spaces, Ann. Inst. Fourier Grenoble38 (1) (1988) 111-132. Zbl0638.47026MR949001
- [9] Kato T., Ponce G., Commutator estimates and the Euler and Navier–Stokes equations, Comm. Pure Appl. Math.41 (1988) 891-907. Zbl0671.35066MR951744
- [10] C. Kenig, K. Koenig, On the local well-posedness of the Benjamin–Ono and modified Benjamin–Ono equations, MRL, submitted for publication. Zbl1044.35072MR2025062
- [11] Kenig C., Ponce G., Vega L., Well-posedness and scattering results for the generalized Korteweg–de Vries equation via the contraction principle, Comm. Pure Appl. Math.46 (1993) 527-620. Zbl0808.35128MR1211741
- [12] Koch H., Tzvetkov N., Local well-posedness of the Benjamin–Ono equation in , IMRN26 (2003) 1449-1464. Zbl1039.35106MR1976047
- [13] Molinet L., Saut J.-C., Tzvetkov N., Well-posedness and ill-posedness results for the Kadomstev–Petviashvili I equation, Duke Math. J.115 (2) (2002) 353-384. Zbl1033.35103MR1944575
- [14] Molinet L., Saut J.-C., Tzvetkov N., Global well-posedness for the KP-I equation, Math. Annalen324 (2002) 255-275. Zbl1008.35060MR1933858
- [15] L. Molinet, J.-C. Saut, N. Tzvetkov, Correction: Global well-posedness for the KP-I equation, Math. Annalen, submitted for publication. Zbl1055.35103
- [16] C. Muscalu, J. Pipher, T. Tao, C. Thiele, Bi-parameter paraproducts, preprint. MR2134868
- [17] Saut J.-C., Remarks on the generalized Kadomstev–Petviashvili equations, Indiana Univ. Math. J.42 (1993) 1011-1026. Zbl0814.35119MR1254130
- [18] Takaoka H., Time local well-posedness for the Kadomstev–Petviashvili II equation, Harmonic Anal. Nonlin. PDE1102 (1999) 1-8. Zbl0951.35520MR1747563
- [19] Tzvetkov N., Global low regularity solutions for Kadomstev–Petviashvili equation, Differential Integral Equations13 (2000) 1289-1320. Zbl0977.35125MR1787069
- [20] Takaoka H., Tzvetkov N., On the local regularity of Kadomstev–Petviashvili-II equation, IMRN8 (2001) 77-114. Zbl0977.35126MR1810481
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