带磁场的广义Zakharov模型的奇异解

数学物理学报 ›› 2022, Vol. 42 ›› Issue (1): 70-85.

带磁场的广义Zakharov模型的奇异解

杨莹¹(),周锐²(),朱世辉^1,*()

¹ 四川师范大学数学科学学院 & 可视化计算与虚拟现实四川省重点实验室成都 610066
² 眉山职业技术学院基础课部四川眉山 620010

收稿日期:2020-07-29 出版日期:2022-02-01 发布日期:2022-02-23
通讯作者: 朱世辉 E-mail:yingyangmath@163.com;zhourui860514@163.com;shihuizhumath@163.com
作者简介:杨莹, E-mail: yingyangmath@163.com|周锐, E-mail: zhourui860514@163.com
基金资助:
国家自然科学基金(12071323);国家自然科学基金(11771314);四川省科技厅应用基础项目(2020YJ0146);四川省科技厅应用基础项目(2020YJ0357)

On the Singular Solutions to a Generalized Magnetic Zakharov Model

Ying Yang¹(),Rui Zhou²(),Shihui Zhu^1,*()

¹ School of Mathematical Sciences and VC&VR Key Lab, Sichuan Normal University, Chengdu 610066
² Department of Normal Education, Meishan Vocational and Technical College, Sichuan Meishan 620010

Received:2020-07-29 Online:2022-02-01 Published:2022-02-23
Contact: Shihui Zhu E-mail:yingyangmath@163.com;zhourui860514@163.com;shihuizhumath@163.com
Supported by:
the NSFC(12071323);the NSFC(11771314);the Sichuan Sciences and Technology Program(2020YJ0146);the Sichuan Sciences and Technology Program(2020YJ0357)

摘要/Abstract

摘要：

该文研究了带磁场的广义Zakharov模型的奇异解.得到了带磁场的广义Zakharov模型奇异解存在的充分条件，以及奇异解的下界速率.

关键词: 带磁场的广义Zakharov模型, 奇异解, 下界速率

Abstract:

In this paper, we consider the singular solutions of a generalized magnetic Zakharov model. The sufficient conditions for the existence of singular solutions, lower bound rate of singular solutions for the generalized magnetic Zakharov model are obtained.

Key words: Generalized magnetic Zakharov model, Singular solution, Lower bound rate

中图分类号:

O175.2

杨莹,周锐,朱世辉. 带磁场的广义Zakharov模型的奇异解[J]. 数学物理学报, 2022, 42(1): 70-85.

Ying Yang,Rui Zhou,Shihui Zhu. On the Singular Solutions to a Generalized Magnetic Zakharov Model[J]. Acta mathematica scientia,Series A, 2022, 42(1): 70-85.

参考文献

1	Daniel H K . From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov. Comm Math Phys, 2013, 324 (3): 961- 993
2	Dendy R O . Plasma Dynamics. Oxford: Oxford University Press, 1990
3	Kono M , Skoric M M , Ter Haar D . Spontaneous excitation of magnetic fields and collapse dynamics in a Langmuir plasma. J Plasma Phys, 1981, 26: 123- 146
4	Zakharov V E . The collapse of Langmuir waves. Soviet Phys, 1972, 35: 908- 914
5	Zakharov V E , Musher S L , Rubenchik A M . Hamiltonian approach to the description of nonlinear plasma phenomena. Phys Rep, 1985, 129 (5): 285- 366
6	Gan Z H , Zhang J . Nonlocal nonlinear Schr?dinger equations in R³. Arch Rational Mech Anal, 2013, 209: 1- 39
7	Laurey C . The Cauchy problem for a generalized Zakharov system. Differ Integral Equa, 1995, 8 (1): 105- 130
8	Miao C X , Zhang B . Harmonic Analysis Method of Partial Differential Equations. Beijing: Science Press, 2008
9	Zhang J Y , Han L J , Guo B L . On the nonlinear Schr?dinger limit of the magnetic Zakharov system. Nonlinear Anal TMA, 2012, 75 (10): 4090- 4103
10	Cazenave T . Semilinear Schr?dinger Equations. Providence RI: Amer Math Soc, 2003
11	韩娅玲, 向建林. 一类分数阶p-Laplace方程基态解的存在性及其渐近行为. 数学物理学报, 2020, 40A (6): 1622- 1633
11	Han Y L , Xiang J L . Existence and asymptotic behavior of ground state for fractional p-Laplacian equations. Acta Math Sci, 2020, 40A (6): 1622- 1633
12	Merle F , Rapha?l P . Blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schr?dinger equation. Ann of Math, 2005, 16: 157- 222
13	肖常旺, 郭飞. 一类半线性波动方程的适定性. 数学物理学报, 2020, 40A (6): 1568- 1589
13	Xiao C W , Guo F . Global existence and blowup phenomena for a semilinear wave equation with time-dependent damping and mass in exponentially weighted spaces. Acta Math Sci, 2020, 40A (6): 1568- 1589
14	Glassey R T . On the blowing up of solutions to the Cauchy problem for nonlinear Schr?dinger equations. J Math Phys, 1977, 18: 1794- 1797
15	Guo B L , Zhang J Y . Well-posedness of the Cauchy problem for the magnetic Zakharov type system. Nonlinearity, 2011, 24: 2191- 2210
16	Zhang J Y , Guo C X , Guo B L . On the Cauchy problem for the magnetic Zakharov system. Monatshefte Fur Mathematik, 2013, 170 (1): 89- 111
17	Gan Z H , Ma Y S , Zhong T . Some remarks on the blow-up rate for the 3D magnetic Zakharov system. J Funct Anal, 2015, 269 (8): 2505- 2529
18	Feng B , Cai Y . Concentration for blow-up solutions of the Davey-Stewartson system in R³. Nonlinear Anal-RWA, 2015, 26: 330- 342
19	Feng B , Ren J , Wang K . Blow-up in several points for the Davey-Stewartson system in R². J Math Anal Appl, 2018, 466 (2): 1317- 1326
20	Li S , Li Y , Yan W . A global existence and blow-up threshold for Davey-Stewartson equations in R³. Discrete Contin Dyn Syst Ser S, 2016, 9 (6): 1899- 1912
21	邱雯, 张贻民, AbdelgadirA A. 一类相对非线性薛定谔方程解的存在性. 数学物理学报, 2019, 39A (1): 95- 104
21	Qiu W , Zhang Y M , Abdelgadir A A . Existence of nontrivial solutions for a class of relativistic nonlinear Schrodinger equations. Acta Math Sci, 2019, 39A (1): 95- 104
22	Zhang J , Zhu S . Sharp blow-up criteria for the Davey-Stewartson system in R³. Dynamics of Partial Differential Equations, 2011, 8 (3): 239- 260
23	Lou S Y , Qiao Z J . Alice-Bob peakon systems. Chinese Physics Letters, 2017, 34: 100201
24	Kwong M K . Uniqueness of positive solutions of δu - u + u^p = 0 in Rⁿ. Arch Rational Mech Anal, 1989, 105: 243- 266
25	Weinstein M I . Nonlinear Schr?dinger equations and sharp interpolation estimates. Comm Math Phys, 1983, 87: 567- 576
26	Oh Y G . Cauchy problem and Ehrenfest's law of nonlinear Schr?dinger equations with potentials. J Differential Equations, 1989, 81: 255- 274
27	Fibich G , Merle F , Rapha?l P . Numerical proof of a spectral property related to singularity formulation for the L²-critical nonlinear Schr?dinger equation. Physica D, 2006, 220: 1- 13
28	Merle F , Rapha?l P . On a sharp lower bound on the blow-up rate for the L²-critical nonlinear Schr?dinger equation. J Amer Math Soc, 2006, 19: 37- 90

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