The Cauchy problem for a generalized Zakharov system
The Cauchy problem for a generalized Zakharov system
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DOI：
10.57262/die/1369143786
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发表时间：
1995-01
影响因子：
1.4
通讯作者：
Corinne Laurey
中科院分区：
文献类型：
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作者：
Corinne Laurey
其中E（t，x）是从R+ Rd到Cd的向量值函数，n（t，x）是从R+ Rd到R的函数，B（t，x）是从R+ Rd到Rd的向量值函数，并且A具有以下形式之一：（A1）A = B，非正常数，或（A2）A = @ @t R Rd B（t，y）|X y|在第二种情况下，将初始数据B（0，x）= B 0（x）加到（1.2）。该系统描述了冷等离子体（情况A1）或热等离子体（情况A2）中磁场的自发产生[8]。E表示高频电场的缓慢变化的复振幅，B表示自生磁场，n表示电子密度从其平衡态的波动，并且n是非负常数，通常为1。忽略磁场B，我们恢复了描述朗缪尔湍流的系统[5]，[16]，|E| 2）= 0。（一、三）
where E(t, x) is a vector valued function from R+ ⇥ Rd into Cd, n(t, x) is a function from R+ ⇥ Rd to R, B(t, x) is a vector-valued function from R+ ⇥ Rd into Rd and A has either the form (A1) A = B, a non positive constant, or (A2) A = @ @t R Rd B(t,y) |x y|2 dy, and in the second case, the initial data B(0, x) = B0(x) is added to (1.2). This system describes the spontaneous generation of a magnetic field in a cold plasma (case A1) or in a hot plasma (case A2) [8]. E denotes the slowly varying complex amplitude of the high-frequency electric field, B the self-generated magnetic field, n the fluctuation of the electron density from its equilibrium, and ↵ is a nonnegative constant, generally ↵ 1. Omitting the magnetic field B, we recover the system describing Langmuir’s turbulence [5], [16], ⇢ iEt + graddivE ↵ rot rotE + nE = 0 ntt (n + |E|2) = 0. (1.3)