-
Previous Article
Ill-posedness for the quadratic nonlinear Schrödinger equation with nonlinearity $|u|^2$
- CPAA Home
- This Issue
-
Next Article
Modified wave operators without loss of regularity for some long range Hartree equations. II
Nonlinear dispersive wave equations in two space dimensions
1. | Department of Mathematics, Graduate School of Science, Osaka University, Osaka Toyonaka 560-0043 |
2. | Department of Mathematics, Graduate School of Science, Osaka University, Osaka, Toyonaka, 560-0043, Japan |
3. | Instituto de Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán, Mexico |
References:
[1] |
P. Brenner, On $L^p-L^q$ estimate of the wave equation, Math. Z., 145 (1975), 251-254. |
[2] |
Y. Cho, T. Ozawa and S. Xia, Remarks on some dispersive estimates, Comm. Pure Appl. Anal., 10 (2011), 1121-1128.
doi: 10.3934/cpaa.2011.10.1121. |
[3] |
J. Ginibre and G. Velo, Generalized Strichartz inequality for the wave equation, J. Funct. Anal., 133 (1995), 50-68.
doi: 10.1006/jfan.1995.1119. |
[4] |
N. Hayashi, Global existence of small solutions to quadratic nonlinear Schrödinger equations, Commun. P.D.E., 18 (1993), 1109-1124.
doi: 10.1080/03605309308820965. |
[5] |
N. Hayashi, S. Kobayashi and P. Naumkin, Global existence of solutions to nonlinear dispersive wave equations, Differential and Integral Equations, 25 (2012), 685-698. |
[6] |
N. Hayashi, C. Li and P. Naumkin, Non existence of asymptotically free solution of systems of nolinear Schrödinger equations, Electron. J. Diff. Equ., 162 (2012), 1-14. |
[7] |
K. Hidano and K. Tsutaya, Global existence and asymptotic behavior of solutions for nonlinear wave equations, Indiana Univ. Math. J., 44 (1995), 1273-1305.
doi: 10.1512/iumj.1995.44.2028. |
[8] |
C. E. Kenig, G. Ponce and L. Vega, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J., 40 (1991), 33-69.
doi: 10.1512/iumj.1991.40.40003. |
[9] |
S. Klainerman, The null condition and global existence to nonlinear wave equations, Lect. Appl. Math., 23 (1986), 293-326. |
[10] |
M. Nakamura, Remarks on Keel-Smith-Sogge estimates and some applications to nonlinear higher order wave equations, Differential and Integral Equations, 24 (2011), 519-540. |
[11] |
T. Ogawa, A proof of Trudinger's inequality and its application to nonlinear Schrödinger equations, Nonlinear Analysis, T.M.A., 14 (1990), 765-769.
doi: 10.1016/0362-546X(90)90104-O. |
[12] |
J-Q. Yao, Comportment à l'infini des solutions d'une équation de Schrödinger non linéaire dans un domaine extérier, C. R. Acad, Sci. Paris, 294 (1982), 163-166. |
show all references
References:
[1] |
P. Brenner, On $L^p-L^q$ estimate of the wave equation, Math. Z., 145 (1975), 251-254. |
[2] |
Y. Cho, T. Ozawa and S. Xia, Remarks on some dispersive estimates, Comm. Pure Appl. Anal., 10 (2011), 1121-1128.
doi: 10.3934/cpaa.2011.10.1121. |
[3] |
J. Ginibre and G. Velo, Generalized Strichartz inequality for the wave equation, J. Funct. Anal., 133 (1995), 50-68.
doi: 10.1006/jfan.1995.1119. |
[4] |
N. Hayashi, Global existence of small solutions to quadratic nonlinear Schrödinger equations, Commun. P.D.E., 18 (1993), 1109-1124.
doi: 10.1080/03605309308820965. |
[5] |
N. Hayashi, S. Kobayashi and P. Naumkin, Global existence of solutions to nonlinear dispersive wave equations, Differential and Integral Equations, 25 (2012), 685-698. |
[6] |
N. Hayashi, C. Li and P. Naumkin, Non existence of asymptotically free solution of systems of nolinear Schrödinger equations, Electron. J. Diff. Equ., 162 (2012), 1-14. |
[7] |
K. Hidano and K. Tsutaya, Global existence and asymptotic behavior of solutions for nonlinear wave equations, Indiana Univ. Math. J., 44 (1995), 1273-1305.
doi: 10.1512/iumj.1995.44.2028. |
[8] |
C. E. Kenig, G. Ponce and L. Vega, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J., 40 (1991), 33-69.
doi: 10.1512/iumj.1991.40.40003. |
[9] |
S. Klainerman, The null condition and global existence to nonlinear wave equations, Lect. Appl. Math., 23 (1986), 293-326. |
[10] |
M. Nakamura, Remarks on Keel-Smith-Sogge estimates and some applications to nonlinear higher order wave equations, Differential and Integral Equations, 24 (2011), 519-540. |
[11] |
T. Ogawa, A proof of Trudinger's inequality and its application to nonlinear Schrödinger equations, Nonlinear Analysis, T.M.A., 14 (1990), 765-769.
doi: 10.1016/0362-546X(90)90104-O. |
[12] |
J-Q. Yao, Comportment à l'infini des solutions d'une équation de Schrödinger non linéaire dans un domaine extérier, C. R. Acad, Sci. Paris, 294 (1982), 163-166. |
[1] |
Kosuke Ono. Global existence and asymptotic behavior of small solutions for semilinear dissipative wave equations. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 651-662. doi: 10.3934/dcds.2003.9.651 |
[2] |
C. I. Christov, M. D. Todorov. Investigation of the long-time evolution of localized solutions of a dispersive wave system. Conference Publications, 2013, 2013 (special) : 139-148. doi: 10.3934/proc.2013.2013.139 |
[3] |
Hongqiu Chen, Jerry L. Bona. Periodic traveling--wave solutions of nonlinear dispersive evolution equations. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 4841-4873. doi: 10.3934/dcds.2013.33.4841 |
[4] |
Fabrício Cristófani, Ademir Pastor. Nonlinear stability of periodic-wave solutions for systems of dispersive equations. Communications on Pure and Applied Analysis, 2020, 19 (10) : 5015-5032. doi: 10.3934/cpaa.2020225 |
[5] |
Jerry L. Bona, Laihan Luo. More results on the decay of solutions to nonlinear, dispersive wave equations. Discrete and Continuous Dynamical Systems, 1995, 1 (2) : 151-193. doi: 10.3934/dcds.1995.1.151 |
[6] |
Honglv Ma, Jin Zhang, Chengkui Zhong. Global existence and asymptotic behavior of global smooth solutions to the Kirchhoff equations with strong nonlinear damping. Discrete and Continuous Dynamical Systems - B, 2019, 24 (9) : 4721-4737. doi: 10.3934/dcdsb.2019027 |
[7] |
Lie Zheng. Asymptotic behavior of solutions to the nonlinear breakage equations. Communications on Pure and Applied Analysis, 2005, 4 (2) : 463-473. doi: 10.3934/cpaa.2005.4.463 |
[8] |
Yongqiang Fu, Xiaoju Zhang. Global existence and asymptotic behavior of weak solutions for time-space fractional Kirchhoff-type diffusion equations. Discrete and Continuous Dynamical Systems - B, 2022, 27 (3) : 1301-1322. doi: 10.3934/dcdsb.2021091 |
[9] |
Zhenhua Zhang. Asymptotic behavior of solutions to the phase-field equations with neumann boundary conditions. Communications on Pure and Applied Analysis, 2005, 4 (3) : 683-693. doi: 10.3934/cpaa.2005.4.683 |
[10] |
Hideo Kubo. Asymptotic behavior of solutions to semilinear wave equations with dissipative structure. Conference Publications, 2007, 2007 (Special) : 602-613. doi: 10.3934/proc.2007.2007.602 |
[11] |
Nakao Hayashi, Pavel I. Naumkin. Asymptotic behavior in time of solutions to the derivative nonlinear Schrödinger equation revisited. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 383-400. doi: 10.3934/dcds.1997.3.383 |
[12] |
Raegan Higgins. Asymptotic behavior of second-order nonlinear dynamic equations on time scales. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 609-622. doi: 10.3934/dcdsb.2010.13.609 |
[13] |
Hiroshi Takeda. Large time behavior of solutions for a nonlinear damped wave equation. Communications on Pure and Applied Analysis, 2016, 15 (1) : 41-55. doi: 10.3934/cpaa.2016.15.41 |
[14] |
Caihong Chang, Qiangchang Ju, Zhengce Zhang. Asymptotic behavior of global solutions to a class of heat equations with gradient nonlinearity. Discrete and Continuous Dynamical Systems, 2020, 40 (10) : 5991-6014. doi: 10.3934/dcds.2020256 |
[15] |
Limei Dai. Entire solutions with asymptotic behavior of fully nonlinear uniformly elliptic equations. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1707-1714. doi: 10.3934/cpaa.2011.10.1707 |
[16] |
P. R. Zingano. Asymptotic behavior of the $L^1$ norm of solutions to nonlinear parabolic equations. Communications on Pure and Applied Analysis, 2004, 3 (1) : 151-159. doi: 10.3934/cpaa.2004.3.151 |
[17] |
Luc Molinet, Francis Ribaud. On global well-posedness for a class of nonlocal dispersive wave equations. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 657-668. doi: 10.3934/dcds.2006.15.657 |
[18] |
Jerry Bona, Hongqiu Chen. Well-posedness for regularized nonlinear dispersive wave equations. Discrete and Continuous Dynamical Systems, 2009, 23 (4) : 1253-1275. doi: 10.3934/dcds.2009.23.1253 |
[19] |
Dongfen Bian, Boling Guo. Global existence and large time behavior of solutions to the electric-magnetohydrodynamic equations. Kinetic and Related Models, 2013, 6 (3) : 481-503. doi: 10.3934/krm.2013.6.481 |
[20] |
Francesca Bucci, Igor Chueshov, Irena Lasiecka. Global attractor for a composite system of nonlinear wave and plate equations. Communications on Pure and Applied Analysis, 2007, 6 (1) : 113-140. doi: 10.3934/cpaa.2007.6.113 |
2020 Impact Factor: 1.916
Tools
Metrics
Other articles
by authors
[Back to Top]