Global solutions of the derivative Schrödinger equation in a class of functions analytic in a strip

Journal of Differential Equations

Volumn 229, Issue 1, 2006, Pages 186-203

  Bona, Jerry L ^a   Grujić, Zoran ^b   Kalisch, Henrik ^c  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

^b UNIVERSITY OF VIRGINIA   (United States)

^c UNIVERSITY OF BERGEN   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746619320     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2006.04.013     Document Type: Article

References (20)

1. Bona J.L., and Grujić Z. Spatial analyticity for nonlinear waves. Math. Models Methods Appl. Sci. 13 (2003) 1-15
2. Bona J.L., Grujić Z., and Kalisch H. Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV-equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005) 783-797
3. Bourgain J. Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. Geom. Funct. Anal. 3 (1993) 107-156 209-262
4. de Bouard A., Hayashi N., and Kato K. Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1995) 673-715
5. Foias C., and Temam R. Gevrey class regularity for the solutions of the Navier-Stokes equations. J. Funct. Anal. 87 (1989) 359-369
6. Ginibre J., Tsutsumi Y., and Velo G. On the Cauchy problem for the Zakharov system. J. Funct. Anal. 151 (1997) 384-436
7. Grujić Z., and Kalisch H. The derivative nonlinear Schrödinger equation in analytic classes. J. Nonlinear Math. Phys. 10 Suppl. 1 (2003) 62-71
8. Hayashi N. Global existence of small analytic solutions to nonlinear Schrödinger equations. Duke Math. J. 60 (1990) 717-727
9. Hayashi N. The initial value problem for the derivative nonlinear Schrödinger equation in the energy space. Nonlinear Anal. 20 (1993) 823-833
10. Hayashi N., and Ozawa T. Finite energy solutions of nonlinear Schrödinger equations of derivative type. SIAM J. Math. Anal. 25 (1994) 1488-1503
11. Hayashi N., and Ozawa T. On the derivative nonlinear Schrödinger equation. Phys. D 55 (1992) 14-36
12. Hayashi N., and Ozawa T. Remarks on nonlinear Schrödinger equations in one space dimension. Differential Integral Equations 7 (1994) 453-461
13. Kato K., and Ogawa T. Analyticity and smoothing effect for the Korteweg-de Vries equation with a single point singularity. Math. Ann. 316 (2000) 577-608
14. Kato T., and Masuda K. Nonlinear evolution equations and analyticity I. Ann. Inst. H. Poincaré Anal. Non Linéaire 3 (1986) 455-467
15. Kenig C.E., Ponce G., and Vega L. Oscillatory integrals and regularity of dispersive equations. Indiana Univ. Math. J. 40 (1991) 33-69
16. Kenig C.E., Ponce G., and Vega L. On the Cauchy problem for the Korteweg-deVries equation in Sobolev spaces of negative indices. Duke Math. J. 71 (1993) 1-20
17. Kenig C.E., Ponce G., and Vega L. Quadratic forms for the 1-D semilinear Schrödinger equation. Trans. Amer. Math. Soc. 348 (1996) 3323-3353
18. Takaoka H. Well-posedness for the one-dimensional nonlinear Schrödinger equation with the derivative nonlinearity. Adv. Differential Equations 4 (1999) 561-580
19. Tsutsumi M., and Fukuda I. On solutions of the derivative nonlinear Schrödinger equation I. Funkcial. Ekvac. 23 (1980) 259-277
20. Tsutsumi M., and Fukuda I. On solutions of the derivative nonlinear Schrödinger equation II. Funkcial. Ekvac. 24 (1981) 85-94