| Title:
|
Initial boundary value problem for generalized Zakharov equations (English) |
| Author:
|
You, Shujun |
| Author:
|
Guo, Boling |
| Author:
|
Ning, Xiaoqi |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
57 |
| Issue:
|
6 |
| Year:
|
2012 |
| Pages:
|
581-599 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper considers the existence and uniqueness of the solution to the initial boundary value problem for a class of generalized Zakharov equations in $(2+1)$ dimensions, and proves the global existence of the solution to the problem by a priori integral estimates and the Galerkin method. (English) |
| Keyword:
|
global solutions |
| Keyword:
|
modified Zakharov equations |
| Keyword:
|
Galerkin method |
| MSC:
|
35A01 |
| MSC:
|
35A02 |
| MSC:
|
35B65 |
| MSC:
|
35L70 |
| MSC:
|
35M33 |
| MSC:
|
35Q40 |
| MSC:
|
35Q55 |
| MSC:
|
76X05 |
| idZBL:
|
Zbl 1274.35305 |
| idMR:
|
MR3010238 |
| DOI:
|
10.1007/s10492-012-0035-6 |
| . |
| Date available:
|
2012-11-10T20:40:12Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143004 |
| . |
| Reference:
|
[1] Garcia, L. G., Haas, F., Oliveira, L. P. L. de, Goedert, J.: Modified Zakharov equations for plasmas with a quantum correction.Phys. Plasmas 12 (2005). 10.1063/1.1819935 |
| Reference:
|
[2] Guo, B., Zhang, J., Pu, X.: On the existence and uniqueness of smooth solution for a generalized Zakharov equation.J. Math. Anal. Appl. 365 (2010), 238-253. Zbl 1185.35275, MR 2585095, 10.1016/j.jmaa.2009.10.045 |
| Reference:
|
[3] Holmer, J.: Local ill-posedness of the 1D Zakharov system.Electron. J. Differ. Equ. 24 (2007), 1-24. Zbl 1115.35124, MR 2299578 |
| Reference:
|
[4] Linares, F., Matheus, C.: Well-posedness for the 1D Zakharov-Rubenchik system.Adv. Differ. Equ. 14 (2009), 261-288. Zbl 1165.35448, MR 2493563 |
| Reference:
|
[5] Linares, F., Saut, J.-C.: The Cauchy problem for the 3D Zakharov-Kuznetsov equation.Discrete Cont. Dyn. Syst. 24 (2009), 547-565. Zbl 1170.35086, MR 2486590, 10.3934/dcds.2009.24.547 |
| Reference:
|
[6] Lions, J.-L.: Quelques méthodes de résolution des problèmes aux limites non linéaires.Dunod/Gauthier-Villars Paris/Paris (1969), French. Zbl 0189.40603, MR 0259693 |
| Reference:
|
[7] Masmoudi, N., Nakanishi, K.: From the Klein-Gordon-Zakharov system to the nonlinear Schrödinger equation.J. Hyperbolic Differ. Equ. 2 (2005), 975-1008. Zbl 1089.35070, MR 2195989, 10.1142/S0219891605000683 |
| Reference:
|
[8] Masmoudi, N., Nakanishi, K.: Energy convergence for singular limits of Zakharov type systems.Invent. Math. 172 (2008), 535-583. Zbl 1143.35090, MR 2393080, 10.1007/s00222-008-0110-5 |
| Reference:
|
[9] Pecher, H.: An improved local well-posedness result for the one-dimensional Zakharov system.J. Math. Anal. Appl. 342 (2008), 1440-1454. Zbl 1140.35307, MR 2445287, 10.1016/j.jmaa.2008.01.035 |
| Reference:
|
[10] You, S.-J.: The posedness of the periodic initial value problem for generalized Zakharov equations.Nonlinear Anal., Theory Methods Appl. 71 (2009), 3571-3584. Zbl 1183.35247, MR 2532737, 10.1016/j.na.2009.01.234 |
| Reference:
|
[11] Zakharov, V. E.: Collapse of Langmuir waves.Sov. Phys. JETP 35 (1972), 908-914. |
| . |
