Zakharov方程组的奇异极限

Singular Limuts of the Zakharov Equations

文中考虑Zakharov方程组Cauchy问题n_(lt)-λ~2△(n+|E|~2)=0iE_l+△E-nE=0n(x,o)=n_0(x),n_l(x,o)=n_1(x),E(x,o)=E_0(x)的奇异极限,即当参数λ→十∞时,方程组和解的极限状态。 借助于等价的变量代换,利用能量估计克服了大参数λ带来的困难,证明了局部c~∞解的存在和唯一性定理.

In this paper we consider the singular limit of the Cauchy Problemof the Zakharov equations n_(tt)- λ~2Δ(n+|E|~2)=0 iE_t+ΔE - nE = 0 n(x, o) = n_0(x), n_t (x, o) = n_1(x), E(x, o) =E_0(x)i. e., the limit state of the equations and solutions as parameter λ→+∞.We took advantage of equivalent variable transform, made use of theestimate of energy, overcame the difficulty by the large Parameter λ,proved the theorem of existence and uniqueness of the local C~∞ solution.