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Global well-posedness of critical nonlinear Schrödinger equations below $L^2$
1. | Department of Mathematics, and Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju 561-756 |
2. | Department of Mathematical Sciences, Seoul National University, Seoul 151-747, South Korea |
3. | Department of Applied Physics, Waseda University, Tokyo 169-8555, Japan |
References:
[1] |
Proc. Amer. Math. Soc., 133 (2005), 3497-3503. |
[2] |
Phys. Rev. E., 62 (2000), 3071-3074. |
[3] |
Annales de l'IHP., 6 (2005), 1-21. |
[4] |
London Mathematical Society Student Texts No. 64, Cambridge University Press, 2005. |
[5] |
Courant Lecture Notes in Mathematics 10, American Mathematical Society, 2003. |
[6] |
Commun. Partial Differential Equations, 35 (2010), 906-943. |
[7] |
Y. Cho and S. Lee, Strichartz estimates in spherical coordinates,, Indiana Univ. Math. J., (). Google Scholar |
[8] |
Nonlinear Analysis TMA, 74 (2011), 2098-2108. |
[9] |
RIMS Kokyuroku Bessatsu, B22 (2010), 145-166. |
[10] |
Commun. Contem. Math., 11 (2009), 355-365. |
[11] |
DCDS-A, 23 (2009), 1273-1290. |
[12] |
J. Func. Anal., 179 (2001), 409-425. |
[13] |
Int. Math. Res. Not. 23 (2007), Art. ID rnm090, 30 pp. |
[14] |
Comm. Pure Appl. Math., 57 (2004), 987-1014. |
[15] |
Forum Math., 23 (2011), 181-205. |
[16] |
Comm. Math. Phys., 151 (1993), 619-645.
doi: 10.1080/15332969.1993.9985061. |
[17] |
J. Funct. Anal., 74 (1987), 160-197.
doi: 10.1016/0022-1236(87)90044-9. |
[18] |
Z. Guo and Y. Wang, Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations,, in preprint, (). Google Scholar |
[19] |
J. Fuctional. Anal., 85 (1989), 307-348. |
[20] |
Commun. Math. Physics, 53 (1977), 285-294. |
[21] |
Funkcial. Ekvac., 51 (2008), 135-147. |
[22] |
Comm. Pure Appl. Math., 60 (2007), 164-186.
doi: 10.1002/cpa.20133. |
[23] |
Amer. J. Math., 120 (1998), 955-980.
doi: 10.1353/ajm.1998.0039. |
[24] |
J. Func. Anal., 219 (2005), 1-20.
doi: 10.1016/j.jfa.2004.07.005. |
[25] |
Ann. Inst. H. Poincaré Phys. Théor, 64 (1996), 33-85. |
[26] |
J. Func. Anal., 253 (2007), 605-627.
doi: 10.1016/j.jfa.2007.09.008. |
[27] |
J. Partial Diff. Eqs., 21 (2008), 22-44. |
[28] |
J. Math. Pure Appl., 91 (2009), 49-79.
doi: 10.1016/j.matpur.2008.09.003. |
[29] |
Ann. I. H. Poincaré Anal. Non Linéaire, 26 (2009), 1831-1852. |
[30] |
Commun. Partial Differential Equations, 36 (2011), 729-776. |
[31] |
Ann. Henri Poincaré, 3 (2002), 503-535. |
[32] |
Math. Ann., 335 (2006), 645-673.
doi: 10.1007/s00208-006-0757-4. |
[33] |
Commun. Partial Differential Equations, 25 (2000), 1471-1485. |
[34] |
Local and global analysis, CBMS 106, eds: AMS, 2006. |
[35] |
J. Opt. Soc. Am. B, 19 (2002), 537-543. |
[36] |
Funkcial. Ekvac., 30 (1987), 115-125. |
[37] |
Springer, New York, 1965. |
show all references
References:
[1] |
Proc. Amer. Math. Soc., 133 (2005), 3497-3503. |
[2] |
Phys. Rev. E., 62 (2000), 3071-3074. |
[3] |
Annales de l'IHP., 6 (2005), 1-21. |
[4] |
London Mathematical Society Student Texts No. 64, Cambridge University Press, 2005. |
[5] |
Courant Lecture Notes in Mathematics 10, American Mathematical Society, 2003. |
[6] |
Commun. Partial Differential Equations, 35 (2010), 906-943. |
[7] |
Y. Cho and S. Lee, Strichartz estimates in spherical coordinates,, Indiana Univ. Math. J., (). Google Scholar |
[8] |
Nonlinear Analysis TMA, 74 (2011), 2098-2108. |
[9] |
RIMS Kokyuroku Bessatsu, B22 (2010), 145-166. |
[10] |
Commun. Contem. Math., 11 (2009), 355-365. |
[11] |
DCDS-A, 23 (2009), 1273-1290. |
[12] |
J. Func. Anal., 179 (2001), 409-425. |
[13] |
Int. Math. Res. Not. 23 (2007), Art. ID rnm090, 30 pp. |
[14] |
Comm. Pure Appl. Math., 57 (2004), 987-1014. |
[15] |
Forum Math., 23 (2011), 181-205. |
[16] |
Comm. Math. Phys., 151 (1993), 619-645.
doi: 10.1080/15332969.1993.9985061. |
[17] |
J. Funct. Anal., 74 (1987), 160-197.
doi: 10.1016/0022-1236(87)90044-9. |
[18] |
Z. Guo and Y. Wang, Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations,, in preprint, (). Google Scholar |
[19] |
J. Fuctional. Anal., 85 (1989), 307-348. |
[20] |
Commun. Math. Physics, 53 (1977), 285-294. |
[21] |
Funkcial. Ekvac., 51 (2008), 135-147. |
[22] |
Comm. Pure Appl. Math., 60 (2007), 164-186.
doi: 10.1002/cpa.20133. |
[23] |
Amer. J. Math., 120 (1998), 955-980.
doi: 10.1353/ajm.1998.0039. |
[24] |
J. Func. Anal., 219 (2005), 1-20.
doi: 10.1016/j.jfa.2004.07.005. |
[25] |
Ann. Inst. H. Poincaré Phys. Théor, 64 (1996), 33-85. |
[26] |
J. Func. Anal., 253 (2007), 605-627.
doi: 10.1016/j.jfa.2007.09.008. |
[27] |
J. Partial Diff. Eqs., 21 (2008), 22-44. |
[28] |
J. Math. Pure Appl., 91 (2009), 49-79.
doi: 10.1016/j.matpur.2008.09.003. |
[29] |
Ann. I. H. Poincaré Anal. Non Linéaire, 26 (2009), 1831-1852. |
[30] |
Commun. Partial Differential Equations, 36 (2011), 729-776. |
[31] |
Ann. Henri Poincaré, 3 (2002), 503-535. |
[32] |
Math. Ann., 335 (2006), 645-673.
doi: 10.1007/s00208-006-0757-4. |
[33] |
Commun. Partial Differential Equations, 25 (2000), 1471-1485. |
[34] |
Local and global analysis, CBMS 106, eds: AMS, 2006. |
[35] |
J. Opt. Soc. Am. B, 19 (2002), 537-543. |
[36] |
Funkcial. Ekvac., 30 (1987), 115-125. |
[37] |
Springer, New York, 1965. |
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