Cauchy problem of the generalized Zakharov type system in \(\mathbf{R}^{2}\)

DOI10.1186/s13660-017-1306-2zbMath1358.35140OpenAlexW2583326072WikidataQ30363263 ScholiaQ30363263MaRDI QIDQ506894

Xiaoqi Ning, Shu-Jun You

Publication date: 2 February 2017

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-017-1306-2

zbMATH Keywords

existenceuniquenessCauchy problemZakharov system

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Statistical mechanics of plasmas (82D10) Quantum hydrodynamics and relativistic hydrodynamics (76Y05) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

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• Stability analysis for Zakharov-Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma
• On the existence and uniqueness of smooth solution for a generalized Zakharov equation
• The posedness of the periodic initial value problem for generalized Zakharov equations
• Energy convergence for singular limits of Zakharov type systems
• Well posedness for the 1D Zakharov-Rubenchik system
• The Cauchy problem for the 3D Zakharov-Kuznetsov equation
• Initial boundary value problem for generalized Zakharov equations.
• On global smooth solution for generalized Zakharov equations
• An improved local well-posedness result for the one-dimensional Zakharov system
• The first integral method for constructing exact and explicit solutions to nonlinear evolution equations

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