| dc.creator | Panthee M. | |
| dc.creator | Scialom M. | |
| dc.date | 2008 | |
| dc.date | 2015-06-30T19:35:33Z | |
| dc.date | 2015-11-26T14:45:57Z | |
| dc.date | 2015-06-30T19:35:33Z | |
| dc.date | 2015-11-26T14:45:57Z | |
| dc.date.accessioned | 2018-03-28T21:55:20Z | |
| dc.date.available | 2018-03-28T21:55:20Z | |
| dc.identifier | | |
| dc.identifier | Advances In Differential Equations. , v. 13, n. 1-2, p. 1 - 26, 2008. | |
| dc.identifier | 10799389 | |
| dc.identifier | | |
| dc.identifier | http://www.scopus.com/inward/record.url?eid=2-s2.0-84894098217&partnerID=40&md5=f046bc5ba0be0a6b20743ffb176c1654 | |
| dc.identifier | http://www.repositorio.unicamp.br/handle/REPOSIP/106774 | |
| dc.identifier | http://repositorio.unicamp.br/jspui/handle/REPOSIP/106774 | |
| dc.identifier | 2-s2.0-84894098217 | |
| dc.identifier.uri | http://repositorioslatinoamericanos.uchile.cl/handle/2250/1252643 | |
| dc.description | We investigate some well-posedness issues for the initial value problem associated to the system for given data in low order Sobolev spaces Hs(R) × Hs(R). We prove local and global well-posedness results utilizing the sharp smoothing es-timates associated to the linear problem combined with the contraction mapping principle. For data with small Sobolev norm we obtain global solution whenever s ≥ 0 by using global smoothing estimates. In particular, for data satisfying where S is solitary wave solution, we get global solution whenever s > 3/4. To prove this last result, we apply the splitting argument introduced by Bourgain [5] and further simplied by Fonseca, Linares and Ponce [6,7]. | |
| dc.description | 13 | |
| dc.description | 1-2 | |
| dc.description | 1 | |
| dc.description | 26 | |
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| dc.description | Alarcon, E., Angulo, J., Montenegro, J.F., Nonlinear Analysis (1999) Stability and instability of solitary waves for a nonlinear dispersive system, 36, pp. 1015-1035 | |
| dc.description | Angulo, J., Bona, J., Linares, F., Scialom, M., Nonlinearity (2002) Scaling, stability and singularities for nonlinear dispersive wave equations: the critical case, 15, pp. 759-786 | |
| dc.description | Bona, J.L., Souganidis, P., Strauss, W., Proc. Roy. Soc. London Ser A (1987) Stability and instability of solitary waves of Korteweg-de Vries type equation, 411, pp. 395-412 | |
| dc.description | Bourgain, J., Internat. Math. Res. Notices (1998) Refinements of Strichartz' inequality and applications to 2D-NLS with critical nonlinearity, 5, pp. 253-283 | |
| dc.description | Fonseca, G., Linares, F., Ponce, G., Communications in PDE (1999) Global well-posedness for the modified Kortewegde Vries equation, 24, pp. 683-705 | |
| dc.description | Fonseca, G., Linares, F., Ponce, G., Proc. Amer. Math. Soc. (2003) Global existence of the critical generalized KdV equation, 131, pp. 1847-1855 | |
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| dc.description | Hakkaev, S., Kirchev, K., (2003) Stability of solitary waves for a nonlinear dispersive system in critical case, , Preprint | |
| dc.description | Kato, T., Studies in Appl. Math. (1983) On the Cauchy problem for the (generalized) Korteweg-de Vries equation, Advances in Mathematics Supplementary Studies, 8, pp. 93-128 | |
| dc.description | Kenig, C.E., Ponce, G., Vega, L., J. Amer. Math. Soc. (1991) Well-posedness of the initial value problem for the Korteweg-de Vries equation, 4 (2), pp. 323-347 | |
| dc.description | Kenig, C.E., Ponce, G., Vega, L., Indiana University Math. J. (1991) Oscillatory integrals and regularity of dispersive equations, 40 (1), pp. 33-69 | |
| dc.description | Kenig, C.E., Ponce, G., Vega, L., Comm. Pure Appl. Math. (1993) Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle, 46, pp. 527-620 | |
| dc.description | Kenig, C.E., Ruiz, A., Trans. Amer. Math. Soc. (1983) A strong type (2,2) estimate for a maximal operator associated to the Schrödinger equation, 230, pp. 239-246 | |
| dc.description | Merle, F., J. Amer. Math. Soc. (2001) Existence of blow-up solutions in the energy space for the critical generalized KdV equation, 14, pp. 555-578 | |
| dc.description | Montenegro, J.F., Estudo local, global e estabilidade de ondas solitarias (1995) Sistemas de equações não-lineares, , Ph. D. Thesis, IMPA, Rio de Janeiro | |
| dc.description | Panthee, M., (2004) Properties of solutions to some nonlinear dispersive models, , Ph. D. Thesis, IMPA, Rio de Janeiro | |
| dc.description | Stein, E., Weiss, G., (1971) Introduction to Fourier Analysis on Euclidean Spaces, , Prince-ton University Press | |
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| dc.language | en | |
| dc.publisher | | |
| dc.relation | Advances in Differential Equations | |
| dc.rights | fechado | |
| dc.source | Scopus | |
| dc.title | On The Cauchy Problem For A Coupled System Of Kdv Equations: Critical Case | |
| dc.type | Artículos de revistas | |
