Global existence of small solutions to nonlinear Schrodinger equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 31, Issue 5-6, 1998, Pages 671-685

  Hayashi, Nakao ^a   Hirata, Hitoshi ^b  

^a TOKYO UNIVERSITY OF SCIENCE   (Japan)

^b SOPHIA UNIVERSITY   (Japan)

Author keywords

Global small solutions; Nonlinear Schr dinger equations

Indexed keywords

FUNCTIONS; INTEGRATION; LINEAR EQUATIONS; MATHEMATICAL OPERATORS; THEOREM PROVING;

SCHRODINGER EQUATIONS; SCHWARZ INEQUALITY; SOBOLEV INEQUALITY; SOBOLEV SPACE; VECTOR FIELD METHOD;

NONLINEAR EQUATIONS;

EID: 0032011541     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00432-X     Document Type: Article

References (17)

1. Klainerman, S., Long-time behavior of solutions to nonlinear evolution equations. Arch. Rat. Mech. Anal., 1982, 78, 73-98.
2. Klainerman, S. and Ponce, G., Global, small amplitude solutions to nonlinear evolution equations. Commun. Pure Appl. Math., 1983, 36, 133-141.
3. Shatah, J., Global existence of small solutions to nonlinear evolution equations. J. Differential Equations, 1982, 46, 409-425.
4. Chihara, H., Global existence of small solutions to semilinear Schrödinger equations with gauge invariance. Publ. RIMS, 1995, 31(5), 731-753.
5. Chihara, H., Global existence of small solutions to semilinear Schrödinger equations. Commun. P.D.E., 1996, 21(1-2), 63-78.
6. Chihara, H., The initial value problem for cubic semilinear Schrödinger equations. Preprint, 1995.
7. Doi, S., On the Cauchy problem for Schrödinger type equations and the regularity of solutions. J. Math. Kyoto Univ., 1994, 34, 319-328.
8. Kenig, C. E., Ponce, G. and Vega, L., Oscillatory integral and regularity of dispersive equations. Indiana Univ. J., 1991, 40, 33-69.
9. Kenig, C. E., Ponce, G. and Vega, L., Small solutions to nonlinear Schrödinger equations. Ann. I.H.P. Non. Lin., 1993, 10, 255-288.
10. Hayashi, N., Global existence of small solutions to quadratic nonlinear Schrödinger equations. Comm. P.D.E., 1993, 18, 1109-1124.
11. Klainerman, S., Uniform decay estimate and the Lorentz invariant of the classical wave equation. Commun. Pure Appl. Math., 1985, 38, 321-332.
12. Kenig, C. E., Ponce, G. and Vega, L., On the generalized Benjamin-Ono equation. Trans. A.M.S., 1994, 342, 155-172.
13. Hayashi, N. and Ozawa, T., Global, small radially symmetric solutions to nonlinear Schrödinger equations and a gauge transformations. Diff. Integral Eqs., 1995, 8, 1061-1072.
14. Hayashi, N. and Kato, K., Global existence of small analytic solutions to quadratic nonlinear Schrödinger equations. Preprint, 1994.
15. Friedman, A., Partial Differential Equations. Krieger, 1983.
16. Ginibre, J. and Hayashi, N., Almost global solutions to quadratic nonlinear Schrödinger equations. Math. Z., 1995, 219, 119-140.
17. Hirata, H., On the elliptic-hyperbolic Davey-Stewartson system. RIMS Kokyuroku, 1994, 873, 140-155.