Sharp threshold of global existence for the generalized Zakharov system with three-dimensional magnetic field in the subsonic limit

被引：0

作者：

Kun Shuai

Juan Huang

Zhigang Pan

机构：

[1] University of Electronic Science and Technology of China,ChengDu College

[2] Sichuan Normal University,College of Mathematics and Software Science

[3] Southwest Jiaotong University,School of Mathematics

来源：

Mathematical Notes | 2015年 / 97卷

关键词：

Zakharov system; magnetic field; subsonic limit; blowup of a solution; global existence;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The paper is concerned with the Zakharov system with three dimensional magnetic field in the subsonic limit, which describes the spontaneous generation of a magnetic field in cold plasma. In fact, we will investigate the effect of the magnetic field term on the equations. By using variational calculus, we obtain the threshold of global existence and blowup of the solution to the equations, which will be more complicated and requires more skill.

引用

页码：450 / 467

页数：17

共 28 条

[1]

Berestycki H.(1981)Instabilitédes états stationnaires dans les équations de Schrödinger et de Klein–Gordon non linéairees C. R. Acad. Sci. Paris 293 489-492

[2]

Cazenave T.(2005)New singular solutions of the nonlinear Schrödinger equation Physica D 211 193-220

[3]

Fibicha G.(2011)Virial type blow-up solutions for the Zakharov system with magnetic field in a cold plasma Journal of Functional Analysis 261 2508-2528

[4]

Gavisha N.(1980)On a class of nonlinear Schrödinger equations with nonlocal interaction Math. Z. 170 109-136

[5]

Wang X. P.(1977)On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations J.Math. Phys. 18 1794-1797

[6]

Gan Z.(1987)On nonlinear Schrödinger equations Ann. Inst. Henri Poincaré, Physique Théorique 49 113-129

[7]

Guo B.(1988)Commutator estimates for the Euler and Navier-Stokes equations Commun. Pure Appl.Math. 41 891-907

[8]

Han L.(1981)Spontaneous excitation of magnetic fields and collapse dynamics in a Langmuir plasma J. Plasma Phys. 26 123-146

[9]

Zhang J.(1995)The Cauchy problem for a generalized Zakharov system Diff. Integral Equ. 8 105-130

[10]

Ginibre J.(1959)On elliptic partial differential equations Ann. della Scuola Norm. Sup. Pisa 13 115-162

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