Artículos de revistas
Global Existence For Schrödinger-debye System For Initial Data With Infinite L2-norm
Registro en:
Quarterly Of Applied Mathematics. American Mathematical Society, v. 73, n. 2, p. 253 - 264, 2015.
0033569X
2-s2.0-84930857109
Institución
Resumen
In this paper we study global-in-time existence for the Cauchy problem associated to the Schrödinger-Debye system for a class of initial data with infinite L2- norm, namely weak-Lp spaces. This model appears in nonlinear optics as a perturbation of the classical nonlinear Schrödinger equation (NLS). Our results exhibit differences between both models in that setting, e.g. the Debye perturbation imposes restrictions in the spatial dimension. We also analyze the asymptotic stability of the solutions. © 2015 Brown University. 73 2 253 264 Arbieto, A., Matheus, C., On the periodic Schrödinger-Debye equation (2008) Commun. Pure Appl. Anal., 7 (3), pp. 699-713 Bennett, C., Sharpley, R., (1988) Interpolation of operators, 129. , Pure and Applied Mathematics, Academic Press Inc., Boston, MA Braz, P., Silva, Ferreira, L.C.F., Villamizar-Roa, E.J., On the existence of infinite energy solutions for nonlinear Schrödinger equations (2009) Proc. Amer. Math. Soc., 137 (6), pp. 1977-1987 Bidégaray, B., On the Cauchy problem for some systems occurring in nonlinear optics (1998) Adv. Differential Equations, 3 (3), pp. 473-496 Bidégaray, B., The Cauchy problem for Schrödinger-Debye equations (2000) Math. Models Methods Appl. Sci., 10 (3), pp. 307-315 Cazenave, T., Weissler, F.B., Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations (1998) Math. Z., 228 (1), pp. 83-120 Corcho, A.J., Linares, F., (2004) Well-posedness for the Schrödinger-Debye equation, 362, pp. 113-131. , Partial differential equations and inverse problems, Contemp. Math., Amer. Math. Soc., Providence, RI Corcho, A.J., Matheus, C., Sharp bilinear estimates and well posedness for the 1-D Schrödinger-Debye system (2009) Differential Integral Equations, 22 (3-4), pp. 357-391 Corcho, A.J., Oliveira, F., Silva, J.D., Local and global well-posedness for the critical Schrödinger- Debye system (2013) Proc. Amer. Math. Soc., 141 (10), pp. 3485-3499 Ferreira, L.C.F., Existence and scattering theory for Boussinesq type equations with singular data (2011) J. Differential Equations, 250 (5), pp. 2372-2388 Kato, T., Fujita, H., On the nonstationary Navier-Stokes system (1962) Rend. Sem. Mat. Univ. Padova, 32, pp. 243-260 Newell, A.C., Moloney, J.V., (1992) Nonlinear optics, , Advanced Topics in the Interdisciplinary Mathematical Sciences, Addison-Wesley Publishing Company Advanced Book Program, Redwood City, CA