Citation: |
[1] |
J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations I. Schrödinger equations, GAFA, 3 (1993), 107-156.doi: 10.1007/BF01896020. |
[2] |
Y. Cho and S. Lee, Strichartz estimates in spherical coordinates, Indi. Univ. Math. J., 62 (2013), 991-1020.doi: 10.1512/iumj.2013.62.4970. |
[3] |
J. Ginibre, Y. Tsutsumi and G. Velo, On the Cauchy problem for the Zakharov system, J. Funct. Anal., 151 (1997), 384-436.doi: 10.1006/jfan.1997.3148. |
[4] |
J. Ginibre and G. Velo, Generalized Strichartz inequalities for the wave equation, J. Funct. Anal., 133 (1995), 50-68.doi: 10.1006/jfan.1995.1119. |
[5] |
Z. Guo and K. Nakanishi, Small energy scattering for the Zakharov system with radial symmetry, Int. Math. Res. Not., 9 (2014), 2327-2342. |
[6] |
Z. Guo, K. Nakanishi and S. Wang, Small energy scattering for the Klein-Gordon-Zakharov system with radial symmetry, Math. Res. Nett., 21 (2014), 733-755.doi: 10.4310/MRL.2014.v21.n4.a8. |
[7] |
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 equation, J. Anal. Math., 124 (2014), 1-38.doi: 10.1007/s11854-014-0025-6. |
[8] |
M. Hadac, S. Herr and H. Koch, Well-posedness and scattering for the KP-II equation in a critical space, Ann. I. H. Poincaré AN, 26 (2009), 917-941.doi: 10.1016/j.anihpc.2008.04.002. |
[9] |
M. Hadac, S. Herr and H. Koch, Erratum to "Well-posedness and scattering for the KP-II equation in a critical space"[Ann. I. H. Poincaré AN, 26 (2009), 917-941], Ann. I. H. Poincar\'e AN, 27 (2010), 971-972.doi: 10.1016/j.anihpc.2008.04.002. |
[10] |
S. Herr, D. Tataru and N. Tzvetkov, Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in $H^1(T^3)$, Duke. Math. J., 159 (2011), 329-349.doi: 10.1215/00127094-1415889. |
[11] |
H. Hirayama, Well-posedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data, Comm. Pure. Appl. Anal., 13 (2014), 1563-1591.doi: 10.3934/cpaa.2014.13.1563. |
[12] |
T. Kato, An $L^{q,r}$-theory for nonlinear Schrödinger equations, Spectral and scattering theory and applications, Adv. Stud. Pure. Math., 23 (1994), 223-238. |
[13] |
I. Kato and K. Tsugawa, Scattering and well-posedness for the Zakharov system at a critical space in four and more spatial dimensions, preprint, arXiv:1512.00551. |
[14] |
J. Kato and T. Ozawa, Endpoint Strichartz estimates for the Klein-Gordon equation in two space dimensions and some applications, J. Math. Pures Appl., 95 (2011), 48-71.doi: 10.1016/j.matpur.2010.10.001. |
[15] |
C. Kenig, G. Ponce and L. Vega, A bilinear estimate with applications to the KdV equation, J. Amer. Soc., 9 (1996), 573-603.doi: 10.1090/S0894-0347-96-00200-7. |
[16] |
M. Keel and T. Tao, Endpoint Strichartz estimates, Amer. J. Math., 120 (1998), 955-980. |
[17] |
H. Koch and D. Tataru, Dispersive estimates for principally normal pseudodifferential operators, Comm. Pure. Appl. Math., 58 (2005), 217-284.doi: 10.1002/cpa.20067. |
[18] |
H. Koch and D. Tataru, A priori bounds for the 1D cubic NLS in negative Sobolev spaces, Int. Math. Res. Not., 16 (2007), article ID rnm053, 36 pages.doi: 10.1093/imrn/rnm053. |
[19] |
H. Lindblad, Counterexamples to local existence for semi-linear wave equations, Amer. J. Math., 118 (1996), 1-16. |
[20] |
H. Lindblad and C. Sogge, On existence and scattering with minimal regularity for semilinear wave equations, J. Funct. Anal., 130 (1995), 357-426.doi: 10.1006/jfan.1995.1075. |
[21] |
S. Machihara, K. Nakanishi and T. Ozawa, Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations, Math. Ann., 322 (2002), 603-621.doi: 10.1007/s002080200008. |
[22] |
S. Machihara, K. Nakanishi and T. Ozawa, Small global solutions and the nonrelativistic limit for the Dirac equation, Rev. Mat. Iberoamericana., 19 (2003), 179-194.doi: 10.4171/RMI/342. |
[23] |
N. Masmoudi and K. Nakanishi, From the Klein-Gordon-Zakharov system to the nonlinear Schrödinger equation, J. Hyperbolic Differ. Equ., 2 (2005), 975-1008.doi: 10.1142/S0219891605000683. |
[24] |
N. Masmoudi and K. Nakanishi, From the Klein-Gordon-Zakharov system to a singular nonlinear Schrödinger system, Ann. I. H. Poincaré AN, 27 (2010), 1073-1096.doi: 10.1016/j.anihpc.2010.02.002. |
[25] |
T. Ozawa, K. Tsutaya and Y. Tsutsumi, Normal form and global solutions for the Klein-Gordon-Zakharov equations, Ann. I. H. Poincaré AN, 12 (1995), 459-503. |
[26] |
T. Ozawa, K. Tsutaya and Y. Tsutsumi, Well-posedness in energy space for the Cauchy problem of the Klein-Gordon-Zakharov equations with different propagation speeds in three space dimensions, Math. Ann., 313 (1999), 127-140.doi: 10.1007/s002080050254. |
[27] |
T. Schottdorf, Global existence without decay for quadratic Klein-Gordon equations, preprint, arXiv:1209.1518. |
[28] |
T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis, in AMS, (2006).doi: 10.1090/cbms/106. |
[29] |
D. Tataru, Local and global results for wave maps I, Comm. Part. Diff. Eq., 23 (1998), 1781-1793.doi: 10.1080/03605309808821400. |