The posedness of the periodic initial value problem for generalized Zakharov equations

You, Shujun

doi:10.1016/j.na.2009.01.234

Cited by 10 publications

(4 citation statements)

References 2 publications

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“…You considered the following initial value problem with period 2 π of generalized Zakharov system:

i E_{t} + E_{x x} - n E + α {false| E false|}^{p} E = 0,

n_{t t} - n_{x x} - {false| E false|}_{x x}^{2} = 0,

with initial data

E |_{t = 0} = E_{0} false(x false), n |_{t = 0} = n_{0} false(x false), n_{t} |_{t = 0} = n_{1} false(x false), x \in false[0, l false],

where the parameters α is a real number. If 0< p <4, the authors obtained the existence and uniqueness of the global classical solution for problem to .…”

Section: Introductionmentioning

confidence: 99%

On the global existence and small dissipation limit for generalized dissipative Zakharov system

Wang

Shang

2018

Math Methods in App Sciences

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This paper deals with the existence and uniqueness of the global solutions to the initial boundary value problem for a generalized Zakharov system with direct self-interaction of the dispersive waves and weak dissipation in the nondispersive subsystem. We prove the global existence of the generalized solution to the problem by a priori estimates and Galerkin method. We also establish the regularity of the global generalized solution and the existence and uniqueness of the global classical solution. Moreover, we obtain the convergence of the solutions of the generalized Zakharov system with dissipation as the dissipative coefficient approaches zero.KEYWORDS approximation of solution, dissipation, existence and uniqueness, generalized Zakharov system, initial boundary value problem, regularity 3718

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“…You considered the following initial value problem with period 2 π of generalized Zakharov system:

i E_{t} + E_{x x} - n E + α {false| E false|}^{p} E = 0,

n_{t t} - n_{x x} - {false| E false|}_{x x}^{2} = 0,

with initial data

E |_{t = 0} = E_{0} false(x false), n |_{t = 0} = n_{0} false(x false), n_{t} |_{t = 0} = n_{1} false(x false), x \in false[0, l false],

where the parameters α is a real number. If 0< p <4, the authors obtained the existence and uniqueness of the global classical solution for problem to .…”

Section: Introductionmentioning

confidence: 99%

On the global existence and small dissipation limit for generalized dissipative Zakharov system

Wang

Shang

2018

Math Methods in App Sciences

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“…This system has been the subject of a large number of studies [3,[5][6][7][8][9][11][12][13][14][15][16]. In addition to the energy method, Zakharov type systems have also been studied by others using different approaches.…”

Section: Introductionmentioning

confidence: 99%

Well-posedness for a class of generalized Zakharov system

You¹,

Ning²

2017

J. Nonlinear Sci. Appl.

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“…In the past decades, the Zakharov system was studied by many authors [2]- [5], [9]- [10]. In [2], B. Guo, J. Zhang, and X. Pu established global in time existence and uniqueness of smooth solution for a generalized Zakharov equation in the two dimensional case for small initial data, and proved global existence of a smooth solution in one spatial dimension without any smallness assumption for the initial data.…”

Section: Introductionmentioning

confidence: 99%

“…If 0 < p < 4, the existence and uniqueness of the global classical solution for a generalized Zakharov equation were obtained in [10]. The nonlinear Schrödinger limit of the Zakharov equation was discussed in [7]- [8].…”

Section: Introductionmentioning

confidence: 99%