Artículos de revistas
Analyticity And Smoothing Effect For The Coupled System Of Equations Of Korteweg-de Vries Type With A Single Point Singularity
Registro en:
Acta Applicandae Mathematicae. , v. 113, n. 1, p. 75 - 100, 2011.
1678019
10.1007/s10440-010-9586-2
2-s2.0-78651273890
Autor
Alves M.S.
Calsavara B.M.R.
Munoz Rivera J.E.
Sepulveda M.
Villagran O.V.
Institución
Resumen
Using Bourgain spaces and the generator of dilation P=3t ∂ t +x ∂ x, which almost commutes with the linear Korteweg-de Vries operator, we show that a solution of the initial value problem associated for the coupled system of equations of Korteweg-de Vries type which appears as a model to describe the strong interaction of weakly nonlinear long waves, has an analyticity in time and a smoothing effect up to real analyticity if the initial data only have a single point singularity at x=0. © 2010 Springer Science+Business Media B.V. 113 1 75 100 Alves, M., Vera Villagrán, O., Smoothing properties for a coupled system of nonlinear evolution dispersive equations (2009) Indag. Math., 20 (2), pp. 285-327. , 1196.35198 10.1016/S0019-3577(09)80015-3 2599818 Ash, J.M., Cohen, J., Wang, G., On Strongly Interacting Internal Solitary Waves (1996) Journal of Fourier Analysis and Applications, 2 (5), pp. 507-517 Bisognin, E., Bisognin, V., Perla Menzala, G., Asymptotic behaviour in time of the solutions of a coupled system of KdV equations (1997) Funkc. Ekvacioj, 40, pp. 353-370. , 0899.35097 1610697 Bisognin, E., Bisognin, V., Sepúlveda, M., Vera, O., Coupled system of Korteweg-de Vries equations type in domains with moving boundaries (2008) J. Comput. Appl. Math., 220, pp. 290-321. , 1158.65056 10.1016/j.cam.2007.08.008 2444171 Bona, J., Ponce, G., Saut, J.C., Tom, M.M., A model system for strong interaction between internal solitary waves (1992) Commun. Math. Phys. Appl. Math., 143, pp. 287-313. , 0752.35056 10.1007/BF02099010 1145797 Bourgain, J., Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, i Schrödinger equation (1993) Geom. Funct. Anal., 3, pp. 107-156. , 0787.35097 10.1007/BF01896020 1209299 Craig, W., Kappeler, T., Strauss, W., Gain of regularity for equations of Korteweg-de Vries type (1992) Ann. Inst. Henri Poincaré, 2, pp. 147-186. , 1160847 Dávila, M., (1995) Continuação Única Para Um Sistema Acoplado de Equações Do Tipo Korteweg-de Vries e Para As Equações de Benjamin-Bona-Mahony e de Boussinesq. Tese de Doutorado, , IM-UFRJ, Brazil Gear, J.A., Grimshaw, R., Weak and strong interactions between internal solitary waves (1984) Commun. Math., 70, pp. 235-258. , 0548.76020 742590 Kato, K., Ogawa, T., Analyticity and smoothing effect for the Korteweg-de Vries equation with a single point singularity (2000) Math. Ann., 316 (3), pp. 577-608. , 0956.35115 10.1007/s002080050345 1752786 Kato, T., On the Cauchy problem for the (generalized) Korteweg-de Vries equations (1983) Adv. Math. Suppl. Stud., Stud. Appl. Math., 8, pp. 93-128 Kato, T., Masuda, K., Nonlinear evolution equations and analyticity. i (1986) Ann. Inst. Henri Poincaré Anal. Non-linéaire, 3, pp. 455-467. , 0622.35066 870865 Kato, T., Ponce, G., Commutator estimates and the Euler and Navier-Stokes equations (1988) Commun. Pure Appl. Math., 41, pp. 891-907. , 0671.35066 10.1002/cpa.3160410704 951744 Kenig, C.E., Ponce, G., Vega, L., A bilinear estimate with applications to the KdV equation (1996) Journal of the American Mathematical Society, 9 (2), pp. 573-603 Kenig, C., Ponce, G., Vega, L., Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction mapping principle (1993) Commun. Pure Appl. Math., 46, pp. 527-620. , 0808.35128 10.1002/cpa.3160460405 1211741 Kenig, C., Ponce, G., Vega, L., On the (generalized) Korteweg-de Vries equation (1989) Duke Math. J., 59 (3), pp. 585-610. , 0795.35105 10.1215/S0012-7094-89-05927-9 1046740 Kenig, C., Ponce, G., Vega, L., Oscillatory integrals and regularity equations (1991) Indiana Univ. Math. J., 40, pp. 33-69. , 0738.35022 10.1512/iumj.1991.40.40003 1101221 Linares, F., Panthee, M., On the Cauchy problem for a coupled system of KdV equations (2004) Commun. Pure Appl. Ann., 3 (3), pp. 417-431. , 1069.35074 10.3934/cpaa.2004.3.417 2098292 Vera, O., (2001) Gain of Regularity for A Generalized Coupled System of Nonlinear Evolution Dispersive Equations Type, , Ph.D. Thesis, UFRJ, Rio de Janeiro, Brazil