Zakharov system in two space dimensions

AbstractWe consider the Zakharov system with quantum effects in the framework of the scalar mode in two space dimensionsiEnVwhich is related to quantum corrections to the Zakharov system for Langmuir waves in plasma. We prove the existence and uniqueness of global smooth solutions to the Cauchy problem for (ZSQ) in the Sobolev space through making a priori integral esimates and utilizing the so-called continuity method.

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The Singular Limit of the Dissipative Zakharov System

Zurnal matematiceskoj fiziki analiza geometrii ◽

10.15407/mag11.01.075 ◽

2015 ◽

Vol 11 (1) ◽

pp. 75-99

Author(s):

A.S. Shcherbina ◽

Keyword(s):

Singular Limit ◽

Zakharov System

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Modification of the vector-field method related to quadratically perturbed wave equations in two space dimensions

Asymptotic Analysis for Nonlinear Dispersive and Wave Equations ◽

10.2969/aspm/08110139 ◽

2019 ◽

Author(s):

Hideo Kubo

Keyword(s):

Vector Field ◽

Wave Equations ◽

Field Method ◽

Two Space Dimensions ◽

Vector Field Method

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A uniformly first-order accurate method for Klein-Gordon-Zakharov system in simultaneous high-plasma-frequency and subsonic limit regime

Journal of Computational Physics ◽

10.1016/j.jcp.2020.110064 ◽

2021 ◽

Vol 428 ◽

pp. 110064

Author(s):

Chunmei Su ◽

Xiaofei Zhao

Keyword(s):

Plasma Frequency ◽

Accurate Method ◽

High Plasma ◽

Zakharov System ◽

First Order ◽

Klein Gordon

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Unconditional uniqueness in the charge class for the Dirac–Klein–Gordon equations in two space dimensions

Nonlinear Differential Equations and Applications NoDEA ◽

10.1007/s00030-012-0196-8 ◽

2012 ◽

Vol 20 (3) ◽

pp. 1055-1063 ◽

Cited By ~ 2

Author(s):

Sigmund Selberg ◽

Achenef Tesfahun

Keyword(s):

Klein Gordon ◽

Two Space Dimensions ◽

Unconditional Uniqueness

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Approximation and Support Theorem for a Wave Equation in Two Space Dimensions

Bernoulli ◽

10.2307/3318761 ◽

2000 ◽

Vol 6 (5) ◽

pp. 887 ◽

Cited By ~ 21

Author(s):

Annie Millet ◽

Marta Sanz-Solé ◽

Marta Sanz-Sole

Keyword(s):

Wave Equation ◽

Support Theorem ◽

Two Space Dimensions

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Finite element collocation method for variably saturated flow in two space dimensions

International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts ◽

10.1016/0148-9062(87)90600-0 ◽

1987 ◽

Vol 24 (3) ◽

pp. 94

Keyword(s):

Finite Element ◽

Collocation Method ◽

Saturated Flow ◽

Two Space Dimensions

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The classical limit of the relativistic Vlasov–Maxwell system in two space dimensions

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.424 ◽

2004 ◽

Vol 27 (3) ◽

pp. 249-287 ◽

Cited By ~ 13

Author(s):

Hayoung Lee

Keyword(s):

Classical Limit ◽

Maxwell System ◽

Two Space Dimensions

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Formation of singularities in compressible fluids in two-space dimensions

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1989-0984811-5 ◽

1989 ◽

Vol 107 (3) ◽

pp. 705-705 ◽

Cited By ~ 24

Author(s):

M. A. Rammaha

Keyword(s):

Compressible Fluids ◽

Two Space Dimensions

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ENERGY CRITICAL NLS IN TWO SPACE DIMENSIONS

Journal of Hyperbolic Differential Equations ◽

10.1142/s0219891609001927 ◽

2009 ◽

Vol 06 (03) ◽

pp. 549-575 ◽

Cited By ~ 24

Author(s):

J. COLLIANDER ◽

S. IBRAHIM ◽

M. MAJDOUB ◽

N. MASMOUDI

Keyword(s):

Schrödinger Equation ◽

Initial Value Problem ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Energy Space ◽

Well Posedness ◽

Initial Value ◽

Exponential Nonlinearity ◽

Supercritical Case ◽

Two Space Dimensions

We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exponential nonlinearity [Formula: see text] We identify subcritical, critical, and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.

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